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[Assistant] You can forget it or remember it, just as you like. I don't see you in the witness box. Ha, quite another shaped box, my good homes, I assure you.


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[Assistant] It matters nothing to me that you should know how my nephew died. It's not him we're talking about, it's you. Yes.


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[Assistant] The fellow who came for me, I forgot his name.


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[Assistant] You are proud of your brains, Holmes. Are you not? Think yourself smart, don't you?


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[Assistant] You came across someone who is smarter this time. Now cast your mind back, Holmes. Can you think of no other way you could have got this thing? I can't think. My mind is gone. For heaven's sake, help me. Yes, I will help you.


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[Assistant] I'll help you to understand just where you are and how you got there. I'd like you to know before you die. Give me something to ease my pain. Painful, is it?


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[Assistant] Yes, the coolies used to do some squealing towards the end. Takes you as cramp, I fancy. Yes.


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[Assistant] Yes, it is cramp. Well, you can hear what I say, anyhow. Listen now.


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[Assistant] Listen, Holmes!" There was a sound as if he was shaking the dying man.


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[Assistant] And it was all that I could do to hold myself quiet in my hiding place.


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[Assistant] You must hear me. You shall hear me. Do you remember a box? An ivory box. It came on Wednesday. You opened it. Do you remember?


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[Assistant] Yes, I opened it. There was a sharp spring inside it. Some joke.


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[Assistant] It was no joke, as you will find to your cost. You fool. You would have had it, and you've got it.


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[Assistant] Who asked you to cross my path? If you'd left me alone, I would not have hurt you." I remember, Holmes gasped. The spring. It drew blood. This box. This on the table. The very one by George, and it may as well leave the room in my pocket. There goes your last shred of evidence.


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[Assistant] But you have the truth now, Holmes, and you can die with the knowledge that I killed you.


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[Assistant] You knew too much of the fate of Victor Savage, so I've sent you to share it.


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[Assistant] You're very near your end, Holmes. I'll sit here and I'll watch you die.


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[Assistant] Ah, the shadows begin to fall, do they? Yes, I'll turn it up, that I may see you the better.


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[Assistant] He crossed the room and the light suddenly brightened.


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[Assistant] Is there any other little service that I can do you, my friend? A match and a cigarette. I nearly called out in my joy and my amazement. He was speaking in his natural voice.


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[Assistant] A little weak perhaps, but the very voice I knew.


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[Assistant] There was a long pause, and I felt that Culverton Smith was standing in silent amazement looking down at his companion.


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[Assistant] What's the meaning of this?" I heard him say at last in a dry, rasping tone.


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[Assistant] The best way of successfully acting a part is to be it," said Holmes. I give you my word that for three days I have tasted neither food nor drink until you were good enough to pour me out that glass of water.


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[Assistant] But it is the tobacco which I find most irksome. Ah, here are some cigarettes. I heard the striking of a match. That is very much better. Hello, hello, do I hear the step of a friend?


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[Assistant] There were footfalls outside. The door opened, and Inspector Morton appeared.


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[Assistant] All is in order, and this is your man," said Holmes. The officer gave the usual cautions. I arrest you on the charge of the murder of one Victor Savage, he concluded.


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[Assistant] And you might add of the attempted murder of one Sherlock Holmes," remarked my friend with a chuckle.


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[Assistant] To save an invalid trouble, Inspector, Mr. Culverton Smith was good enough to give our signal by turning up the gas.


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[Assistant] By the way, the prisoner has a small box in the right-hand pocket of his coat, which it would be as well to remove. Thank you. I would handle it gingerly if I were you. Put it down here. It may play a part in the trial.


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[Assistant] There was a sudden rush and a scuffle, followed by the clash of iron and a cry of pain.


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[Assistant] You'll only get yourself hurt, said the inspector. Stand still, will you? There was a clicking of the closing handcuffs.


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[Assistant] You can lie as you like, Mr. Holmes. My word is always as good as yours.


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[Assistant] Good heavens! cried Holmes. I had totally forgotten him.


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[Assistant] My dear Watson, I owe you a thousand apologies. To think that I should have overlooked you.


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[Assistant] I need not introduce you to Mr. Culverton Smith, since I understand that you met somewhat earlier in the evening. Have you the cab below? I will follow you when I am dressed, for I may be of some use at the station.


[User] Please transcribe this text

[Assistant] I never needed it more," said Holmes as he refreshed himself with a glass of claret and some biscuits in the intervals of his toilet.


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[Assistant] However, as you know, my habits are irregular, and such a feat means less to me than to most men. It was very essential that I should impress Mrs. Hudson with the reality of my condition, since she was to convey it to you, and you in turn to him.


[User] Please transcribe this text

[Assistant] You won't be offended, Watson. You will realize that among your many talents dissimulation finds no place, and that if you had shared my secret you would never have been able to impress Smith with the urgent necessity of his presence, which was the vital point of the whole scheme.


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[Assistant] Knowing his vindictive nature, I was perfectly certain that he would come to look upon his handiwork. But your appearance, Holmes! Your ghastly face!


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[Assistant] Three days of absolute fast does not improve one's beauty, Watson.


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[Assistant] For the rest there is nothing which a sponge may not cure. With vaseline upon one's forehead, belladonna in one's eyes, rouge over the cheekbones, and crusts of beeswax round one's lips, a very satisfying effect can be produced.


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[Assistant] Malingering is a subject upon which I have sometimes thought of writing a monograph. A little occasional talk about half-crowns, oysters, or any other extraneous subject produces a pleasing effect of delirium.


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[Assistant] But why would you not let me near you, since there was in truth no infection? Can you ask, my dear Watson?


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[Assistant] Do you imagine that I have no respect for your medical talents?


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[Assistant] Could I fancy that your astute judgment would pass a dying man who, however weak, had no rise of pulse or temperature? At four yards I could deceive you. If I failed to do so, who would bring Mr. Smith within my grasp? No, Watson?


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[Assistant] I would not touch that box. You can just see if you look at it sideways, where the sharp spring like a viper's tooth emerges as you open it.


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[Assistant] I dare say it was by some such device that poor Savage, who stood between this monster and the reversion, was done to death. My correspondence, however, is, as you know, a varied one, and I am somewhat upon my guard against any packages which reach me. It was clear to me, however,


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[Assistant] But by pretending that he had really succeeded in his design, I might surprise a confession.


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[Assistant] That pretense I have carried out with the thoroughness of the true artist.


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[Assistant] Thank you, Watson. You must help me on with my coat. When we have finished at the police station, I think that something nutritious at Simpson's would not be out of place.


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[Assistant] End of the adventure of the dying detective.


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[Assistant] But she just wants a hug from her daddy. And dad can never say no.


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[Assistant] Goma is always goofing off with her daddy. He really is the nicest dad.


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[Assistant] Wow, what a view. Good night, Goma and company.


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[Assistant] Wait, she swallows everything full? Yep. Her sharp teeth are for trapping prey. Not for chewing. Her stomach does all the work.


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[Assistant] Come on little guy, listen to your mom. It's so nice outside.


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[Assistant] Look, they're starting to look like grown-ups. The shy ones stay close to mom, but Lobo is going on an adventure.


[User] Please transcribe this text

[Assistant] What's that otter doing? Hmm, that looks good.


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[Assistant] Just as you can use Words Replace feature to locate and replace one text string with another, you can use Replace to replace one style with another. And I want to show you two different examples of why you might choose to do this.


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[Assistant] The first is a replacement where we would like to replace all of the instances in a document of one type of body text, for example, with another. If, for example, I wanted to have all the text that was currently normal


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[Assistant] Replace with no spacing. I could do that piece by piece. I could go select this and I could choose no spacing and I could continue to do this paragraph by paragraph.


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[Assistant] But because I have other formatting, it's not like I can simply select all the body text. I can't. And because I can't, this becomes a manual process. Not a good idea if I can avoid it. Let's see what Replace brings to the table for us. Find what? Well, this is where I would enter text, but click the More button.


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[Assistant] And tell it that you are actually looking for a format. And the style you're looking for is normal.


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[Assistant] When it finds normal, tell it to replace it with a different style.


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[Assistant] And the different style we would like to replace it with is no spacing.


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[Assistant] This will be subtle because all that's going to change really is the spacing, but let's tell it that we would like to replace.


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[Assistant] Notice the first paragraph has been replaced and I can continue to go from one paragraph to the next or I could simply choose replace all. It looks like it knows what it's doing for replacement sounds right. Yes, we're all done.


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[Assistant] So in this case, what I have done is replace one style normal with another consistently throughout the document.


[User] Please transcribe this text

[Assistant] I can go back to the start of the document again and reverse this, or I could choose undo to get rid of it. But it's a very quick and easy thing for me to do.


[User] Please transcribe this text

[Assistant] To say, in this case what I'd like to do is replace the style, no spacing,


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[Assistant] Notice I can't choose two styles at once, right? So it automatically says, well, she doesn't want to do normal anymore. And in this case, it replaced no spacing with normal. And let's simply replace them all. All done. Looks good.


[User] Please transcribe this text

[Assistant] The styles throughout a document or have an automated process for choosing on a case by case basis where I would like to replace a style.


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[Assistant] The second choice happens far more frequently to me. I have this wonderful outline. I have a document laid out.


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[Assistant] For our residential installation summary, and I get a knock on the door that says your report's going to include commercial installations as well.


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[Assistant] That's interesting because now residential installations


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[Assistant] Will become a heading one in a new combined document.


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[Assistant] As long as I start with the lowest level of heading I have and work my way up, I can do this automatically. Let's replace all of my heading 1s, that's the lowest level of heading I'm using in my document, with heading 2s.


[User] Please transcribe this text

[Assistant] Heading 1. Now notice that there's also a Heading 1 character. This will only replace the character as opposed to the paragraph style. Remember that headings are linked styles.


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[Assistant] So this says replace it on a character basis, and here it is, replace the style as a whole, which is what I want. I want my heading ones to now become heading twos. Replace format style, heading two.


[User] Please transcribe this text

[Assistant] Okay. I'll usually do the first one using just replace.


[User] Please transcribe this text

[Assistant] That worked. My Heading 1 is now a Heading 2. If I click here, there's my Heading 2, rather than a Heading 1. Cool. Go replace them all.


[User] Please transcribe this text

[Assistant] And there were three left and they've all been done. Sweet.


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[Assistant] Now if I wished, I could then replace my title with a heading 1.


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[Assistant] I don't need to do that. There's only one title. Simply drop in here. Make it a heading one. And I'm now ready.


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[Assistant] To add the rest of the content and provide a new title for this report.


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[Assistant] With the judicious use of the replace function and using either replace or replace all, I can use the replace tool to easily reformat my document by swapping one style for another without the need to do it manually.


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[Assistant] Bob's bored without his sister, just like you when I'm not there, right Tim? Go on, go find Lily. Bye bye Bob.


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[Assistant] At the end of each conversation, you will hear four questions. Both the conversation and the questions will be spoken only once. After you hear a question, you must choose the best answer from the four choices marked A, B, C and D.


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[Assistant] Then mark the corresponding letter on answer sheet 1 with a single line through the centre.


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[Assistant] How can it be just okay when last week you were thrilled about the place and kept posting photos of it online?


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[Assistant] That's the problem. You miss your roommates from university, don't you?


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[Assistant] When I got my first place, I remember thinking I couldn't wait to live by myself and get away from my juvenile roommates and all their annoying habits.


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[Assistant] But then I began missing them and feeling lonely and thinking that our dormitory was like paradise.


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[Assistant] Even though there were six of us guys in one small room.


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[Assistant] You lived at home with us, and then you had three roommates. And this is your first time living alone. So it's hard.


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[Assistant] But your first apartment is a milestone in your life, and you should celebrate it. Tell me about the apartment.


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[Assistant] That does sound adorable, and I can't wait to see it, and neither can Mum and Dad.


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[Assistant] Questions 1 to 4 are based on the conversation you have just heard. Question 1.


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[Assistant] What was the woman's first impression of the apartment?


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[Assistant] Why does the woman say she is going to sound like an idiot?


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[Assistant] What do we learn about the man when he left the dormitory to live on his own?


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[Assistant] What does the man say he can't wait to do?


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[Assistant] Yes, I believe that the purpose of higher education is to prepare young people to enter the workforce, and that our current system fails to do this.


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[Assistant] We're allocating too many resources to disciplines that don't match the needs of employers.


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[Assistant] Many young graduates struggle to find any job, let alone a good one.


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[Assistant] The job market is grim, particularly for students who study the arts.


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[Assistant] You're overstating my point. My argument is that we need to use more of our budget on areas like science and engineering.


[User] Please transcribe this text

[Assistant] To do that, we need to take money from subjects like literature and music.


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[Assistant] I agree that the arts are valuable to society.


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[Assistant] But it's naive to think that not only the most talented, but all students should study them at university level.


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[Assistant] The arts are very competitive and most graduates will end up with a great deal of debt obtaining a degree that has little value on the job market.


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[Assistant] Directions. In this section, you'll hear two passages.


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[Assistant] At the end of each passage, you will hear three or four questions. Both the passage and the questions will be spoken only once. After you hear a question, you must choose the best answer from the four choices marked A, B, C and D.


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[Assistant] Questions 9 to 11 are based on the passage you have just heard. Question 9.


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[Assistant] What do we learn about the feeling that one doesn't have time to think anymore?


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[Assistant] What trait do all great professionals share?


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[Assistant] What do some researchers believe is conducive to creative ideas?


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[Assistant] Even before Colorado was a state, it had post officers.


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[Assistant] The first opened in 1859 in a settlement founded by migrants searching for gold. Life could be unpredictable out west. Gold failed to appear.


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[Assistant] Drought ruined farmers, and settlers clashed with Native Americans.


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[Assistant] On the settlement's location now stands a sprawling university campus.


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[Assistant] Amid all the changes, one feature remained constant, the postal service.


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[Assistant] The maps tracing America's westward expansion are telling.


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[Assistant] In 1864, there were few postal branches on land controlled by Native Americans, which still accounted for most of the West.


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[Assistant] Over the next 25 years, post officers grew quickly.


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[Assistant] Colonization of the West could be regarded as a result of big government rather than pioneers.


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[Assistant] As federal subsidies and land grants tempted people into the deserts and plains, the Post kept them connected.


[User] Please transcribe this text

[Assistant] In the mid 19th century, the post office department was far from a centralized bureaucracy. To keep up with migration patterns,


[User] Please transcribe this text

[Assistant] Postal services were added to existing businesses.


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[Assistant] The federal government commissioned private wagons to carry the mail.


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[Assistant] Short term contracts were granted to local businessmen to act as postmasters.


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[Assistant] These partnerships enable the mail to quickly follow migrants, helping knit together remote parts of the country.


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[Assistant] Mr. Belvins, a digital historian, wrote a book on the history of the US Postal Service.


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[Assistant] He used data science to analyze historical trends.


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[Assistant] Most strikingly, he built an accompanying website, complete with interactive maps.


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[Assistant] They show readers how within a generation the postal service helped colonise a continent.


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[Assistant] These online interactive maps illustrate the formative power of snail mail.


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[Assistant] In this section you will hear three recordings of lectures or talks, followed by three or four questions.


[User] Please transcribe this text

[Assistant] The recordings will be played only once. After you hear a question, you must choose the best answer from the four choices marked A, B, C and D. Then mark the corresponding letter on answer sheet one with a single line through the centre.


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[Assistant] Question 16 to 18 are based on the recording you have just heard. Question 16.


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[Assistant] What does the speaker say the new study suggests?


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[Assistant] What did researchers do first in the new study?


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[Assistant] What do we learn from previous studies about anxiety?


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[Assistant] Over the past 20 years, the internet has gradually become a dominant feature of our lives. It has changed how we communicate with each other.


[User] Please transcribe this text

[Assistant] And it has definitely transformed the way we do business with each other.


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[Assistant] Marketing has also changed in a number of ways. For instance,


[User] Please transcribe this text

[Assistant] In the past, consumers had to call a phone number and patiently wait on hold in order to get the information they wanted. Today, they want the information immediately.


[User] Please transcribe this text

[Assistant] They'll go to the company's social media page and post comments and questions expecting to receive an immediate response.


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[Assistant] If they don't get their questions answered soon, they'll move on to another company that will answer them quickly.


[User] Please transcribe this text

[Assistant] Marketing departments today need to follow technological development.


[User] Please transcribe this text

[Assistant] For example, this year's smartphone is smarter than last year's. Self driving cars are now on the road.


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[Assistant] Marketers have to do research on which technologies are coming into being. Otherwise, they risk being left behind in the virtual dust.


[User] Please transcribe this text

[Assistant] Marketing has also changed due to the importance of video.


[User] Please transcribe this text

[Assistant] People don't just want to read text, they want to watch things happening.


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[Assistant] Companies now have to explore how they can use video on a consistent basis to share information about their businesses.


[User] Please transcribe this text

[Assistant] Fortunately, it's extremely easy to shoot something these days. All you need is a smartphone. But what's the result of all this? Shorter attention spans.


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[Assistant] We aren't the same people that we were 20 years ago.


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[Assistant] Not only have we grown accustomed to getting the information we want instantaneously, our attention spans are much shorter.


[User] Please transcribe this text

[Assistant] If something doesn't capture our attention within a few seconds, we're on to the next piece of content.


[User] Please transcribe this text

[Assistant] Marketers need to figure out ways to speak directly to the customer's emotions and they need to figure out how to do that as quickly as possible.


[User] Please transcribe this text

[Assistant] Once people are emotionally engaged, they'll stick with you.


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[Assistant] If marketing has changed this much in the past 20 years, imagine what the next 20 years will bring.


[User] Please transcribe this text

[Assistant] In a recent survey, only 9% of marketers could say with confidence that their marketing efforts were actually working.


[User] Please transcribe this text

[Assistant] Their confidence is being shaken because the rules of the game change every year.


[User] Please transcribe this text

[Assistant] That's why it's important for marketers to pay attention to the latest technological developments.


[User] Please transcribe this text

[Assistant] And consider collaborating with technological innovators.


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[Assistant] That way, they'll be moving at the same pace as the tech industry.


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[Assistant] Questions 22 to 25 are based on the recording you have just heard. Question 22. What does the speaker say is interesting?


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[Assistant] What did researchers from an American university analyze in their initial study?


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[Assistant] What did the second study find about non-work friends?


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[Assistant] What does the speaker suggest managers do?


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[Assistant] If I look for example at normal style, notice that not only does it have a font and an alignment, it also has spacing. Spacing within a paragraph called line spacing. Spacing before or after a paragraph. If I look at a heading, it may also have spacing as well or it could inherit the spacing


[User] Please transcribe this text

[Assistant] It's not part of themes, but it hangs out on the design tab, and I'd like to show you how it works. It's called paragraph spacing. And if I click the paragraph spacing dropdown,


[User] Please transcribe this text

[Assistant] Notice that default spacing which we're using now says that there will be zero points before a paragraph, eight points after, and the line spacing right now for my default is 1.08.


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[Assistant] But if I wanted to make it more compact, I can. These are arranged in order from very tight to very loose. No paragraph spacing. Compact. Tight. Open.


[User] Please transcribe this text

[Assistant] Once I get to open, I now have ten points after each paragraph.


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[Assistant] Relaxed. Even more spacious. Really good for something I'm going to read aloud like a speech. And then double which is sometimes used for academic papers or reports. I can also create my own custom paragraph spacing if I wish. But normally the choice that I want to make is something that I can find here.


[User] Please transcribe this text

[Assistant] Rather than adjusting individual styles or individual sections of text,


[User] Please transcribe this text

[Assistant] I can adjust the spacing within and between paragraphs for the entire document by using the paragraph spacing command here on the design tab.


[User] Please transcribe this text

[Assistant] Uh, don't you birds know you're supposed to be asleep? Uh, nighttime is my time.


[User] Please transcribe this text

[Assistant] You know, the moon looks like all of these shapes sometimes. And, uh, sometimes it's not there at all. Like, uh, tonight.


[User] Please transcribe this text

[Assistant] Now we have an oscillating. Exponentials, the previous lecture, grew or decayed. Now we have an oscillating. We have AC, alternating current in this problem. Instead of, uh, expo- pure expo- instead of real exponentials, we have oscillation.


[User] Please transcribe this text

[Assistant] The particular solution, it would be nice if we could say the particular solution was just some multiple of the cosine.


[User] Please transcribe this text

[Assistant] But that won't work. So that makes this problem one step harder than the exponential. We need to allow the sines in there. Because if I look for a cosine, if I tried only this part,


[User] Please transcribe this text

[Assistant] That, I could match that. I could, I'd have a times the cosine. That would be cosines. But the derivative of a cosine is a sine function.


[User] Please transcribe this text

[Assistant] Okay, so that's the right thing to assume. Actually, there will be, you'll see, three different ways to write the answer to this problem. And this is the first, sort of most straightforward, but not


[User] Please transcribe this text

[Assistant] The derivative brought out this factor omega, the derivative of cosine was sine. Now the derivative of this brings out a factor of omega, omega n, cosine omega t, and that should equal


[User] Please transcribe this text

[Assistant] That's the ay part, and now I have the source term plus cosine omega t. And that has to be true for all time, and


[User] Please transcribe this text

[Assistant] That cosine term and the source term, so they all multiply cosine omega t, so I want omega n.


[User] Please transcribe this text

[Assistant] Should I bring this over on the other side? Minus A M.


[User] Please transcribe this text

[Assistant] Plus omega n equals, uh, here I just have one cosine equals one.


[User] Please transcribe this text

[Assistant] Minus a m plus omega n equals 1. And now I'll match the sine terms. So in the sine terms I have a minus omega m, sine omega t,


[User] Please transcribe this text

[Assistant] And I have to bring this on the other side, so that'll be a minus a n sine omega t. And there's no sine omega t in the source. There's my two equations.


[User] Please transcribe this text

[Assistant] Those are my two equations for m and n. So I just solve those two equations and I've got the particular solution that I look for.


[User] Please transcribe this text

[Assistant] So, it's two equations, two unknowns, it's the basic problem of linear algebra. I'm inclined to just write down the answer, which I prepared in advance.


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[Assistant] M, it turns out to be minus A over omega squared plus A squared.


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[Assistant] And n turns out to have that same omega squared plus a squared, and above it goes omega.


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[Assistant] Omega times the m will give me an a omega with a minus with a minus and then a times n will also be have an a omega.


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[Assistant] It, I get, they cancel to give zero. And this equation is also solved. So, one more important problem solved.


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[Assistant] Now in many many cases, it's this particular solution that's of interest. This here, let me put a box around our solution.


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[Assistant] And we substituted that in the differential equation. We discovered m. We discovered n. We've got this particular solution. And, and that's the sort of, that's the oscillation.


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[Assistant] That's called the transient term, so the null solution would be having e to the a t as always.


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[Assistant] But, I'm not so interested in that. It's, uh, because it disappears. You don't hear it after a minute. And, and this is the solution that you're, this is what your ear is hearing. Okay. So we've got one form of the answer.


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[Assistant] No, that's a pretty nice form, but it's not perfect.


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[Assistant] I believe that that same YP of T can be written in a different way as what also, uh, another, another form, a different


[User] Please transcribe this text

[Assistant] This will be the same y of t.


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[Assistant] So, because those are out of phase and they're combining into something and I want to find out what they're combining into. And it's really nice. They're combining into a single cosine, but not just omega t, it's


[User] Please transcribe this text

[Assistant] Or often it would be called capital R just for, uh, because it's some sort of what you're seeing here is polar coordinates. So I want to match


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[Assistant] This, which has the g and the alpha,


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[Assistant] G and an alpha, a magnitude and an angle.


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[Assistant] I want to match that with the form I already had.


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[Assistant] I'll use a little trigonometry here to remember that this is equal to, I have a G.


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[Assistant] Do you remember a formula for the cosine of A minus B, the cosine of a difference, is cosine of omega t cosine of alpha plus, it's a plus here because it's a minus there, sine omega t sine alpha.


[User] Please transcribe this text

[Assistant] So I have just written this out in the two-term form, and I did that so that I could match the two-term form I already had. So can I just do that matching? The cosine omega t, the m, must be g cos alpha.


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[Assistant] Fundamental identity when you see cosines and sines is to remember that cosine squared plus sine squared is one. I'm gonna use that, have to use it. So I'll square both sides, I'll have m squared, and, and I'll add.


[User] Please transcribe this text

[Assistant] So I'll have m squared plus n squared.


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[Assistant] It is g squared, cosine squared alpha.


[User] Please transcribe this text

[Assistant] g squared times cosine squared alpha when I squared that one and sine squared alpha


[User] Please transcribe this text

[Assistant] So what have I learned? g is the square root of this. g is the square root of m squared plus n squared.


[User] Please transcribe this text

[Assistant] So I have to have to, again, I'm thinking trig here. How am I going to get alpha here? I want to get g out of this formula now and just focus on the alpha.


[User] Please transcribe this text

[Assistant] Previously I got alpha out of it and got the g. Now, the way to do it is, take the ratio. If I take the ratio of that to that, divide one by the other, the g's will cancel, so I'll take the ratio of that to that to get


[User] Please transcribe this text

[Assistant] Sine over cosine is tangent of alpha is n over n.


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[Assistant] Any mixture of sines and cosines of the same, uh, omega t.


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[Assistant] So, so the sinusoidal identity says that that I can rewrite that solution into this solution.


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[Assistant] And I really see the key number in the whole thing is the gain, the magnitude. It's how loud the station comes through if we're tuning a radio. So, uh, and again this is the response that keeps going because the cosine oscillates forever.


[User] Please transcribe this text

[Assistant] There will be also, uh, something coming from the initial condition that we expect to die out. Okay, so I mentioned at the very start that there were three forms of the answer to this sine of sine, cosine input. And I've given you two. I've given you the m and n form.


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[Assistant] You could say rectangular coordinates, cosines and sines. I've given you the polar form.


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[Assistant] Which is, uh, a gain, a magnitude and a phase. And the third one involves complex numbers. I have to make that a separate lecture. Maybe even two.


[User] Please transcribe this text

[Assistant] So complex numbers, uh, where do they come in? It's a totally real equation. If I think about all this that I've done, it was all totally real, but, uh,


[User] Please transcribe this text

[Assistant] I can, I, I get, there's a link, the key fact about complex numbers. Euler's great formula will give me a connection between cosine omega t and sine omega t with e to the i omega t. So,


[User] Please transcribe this text

[Assistant] At the price of introducing that complex number, imaginary number i,


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[Assistant] Or J for, for, uh, electrical engineers. We have, uh, s- we're back to exponentials.


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[Assistant] So this is the source function here and it was nice.


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[Assistant] Exponential was even nicer. Constant was best of all. And I want to, another one I want to introduce is a delta function. So that's a, a delta function is an impulse, something that happens in an instant. And that's an interesting, very interesting and very important possibility. Okay, thank you.


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[Assistant] If I'm interested in recording, I should learn it.


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[Assistant] Huh? I heard peep again! With my sensitive duck hearing! This way!


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[Assistant] I guess picnics aren't that interesting after all. Look Chirp!


[User] Please transcribe this text

[Assistant] Journey to the West, Chapter 2, The Waterfall Cave.


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[Assistant] The cave was filled with bamboo trees and beautiful flowers. Moss covered the walls.


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[Assistant] Monkey found a long table with bowls, cups, and plates. A fireplace sat against one wall.


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[Assistant] Deeper in the cave, Monkey found bedrooms with cozy beds.


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[Assistant] Outside. The other monkeys and apes were looking at the waterfall.


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[Assistant] Soon all of the monkeys and apes were in the cave. Everyone ran around to see all the wonderful things.


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[Assistant] Said the gibbon. He bowed to Monkey and said,


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[Assistant] Said monkey. The gibbon rubbed his chin.


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[Assistant] As the raft began to float away, Monkey waved to his friends.


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[Assistant] You were probably created by heaven and earth. You may be my student. You need a name.


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[Assistant] I love learning from you. Wukong, you have been here a long time. What would you like to learn from me?


[User] Please transcribe this text

[Assistant] I can teach you how to tell the future. Would you like that?


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[Assistant] How about some magic breathing exercises?


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[Assistant] Style is definitely not one size fits all. It's something that you develop and that is something very personal and you will work on for years, decades. This is, this is a lifelong process and it should evolve as you do.


[User] Please transcribe this text

[Assistant] Style is an extension of you. It's a part of you. It's gonna make you feel a certain way. Tend to it. Care for it. Make sure it's nurtured. And so, that means checking in on it regularly. Yes, it may feel good.


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[Assistant] Buy something you wouldn't ordinarily buy and at least try it. Continue to invest in your salon. I'm not talking about a lot of money. I'm talking about investing the time to make sure that you still feel that same kind of newness, that same kind of excitement about what you're putting on your body every day.


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[Assistant] I see style as ever evolving for anyone, including myself. Even though I style for a living, that is constantly evolving. I never want it to become stale.


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[Assistant] What I wish somebody had taught me was that I didn't have to embrace every trend. When I was younger, especially at college and in my first couple of jobs, I thought, oh, I've got to keep up with the trends. I've got to seem like a cool kid.


[User] Please transcribe this text

[Assistant] And now I look back thinking, what a plonker. You do not need to participate in trends in order to be stylish. However, trends are a really fun part of style. So incorporate one or two as you feel comfortable. Don't go crazy with it.


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[Assistant] Play with it. See it as an extension of your current closet and of your current style.


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[Assistant] When there's a new trend that comes out, I will at least experiment with many of them. Even if I know there's no way I'm going to wear 16 of these, but I may find one and so I will try it and mix it into my regular wardrobe, my capsule wardrobe and find a way of incorporating it that makes it feel like me.


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[Assistant] You stick to that rule of who do I want to be, what do I want to portray, and you won't go wrong. You won't fall victim to all of these trends.


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[Assistant] Trends are changing constantly. They actually change at a much faster rate these days than they did 15 years ago before we had social media and very easy access to the internet.


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[Assistant] Back in the day, a trend would last roughly around about six months, and you'd know we'd move on to something else quite soon after that. However, these days with fast fashion in particular, you can have a new trend every three or four weeks. As quickly as they can produce a new trend, you will have a new trend on the streets. Don't spend money on a trend.


[User] Please transcribe this text

[Assistant] Find the cheapest option you can find of that trend if you desperately want to incorporate it into your wardrobe. Spending so much money on a trend really is throwing money away. You may as well literally burn it. I would rather you spend that money on something that you know you will wear for at least the next few years. The way that I see trend versus classic is


[User] Please transcribe this text

[Assistant] Therefore, is it a classic? Probably yes. Is this new? Is this something that feels exciting? Am I seeing every cool kid around town wearing it?


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[Assistant] Probably a trend. Do I want to invest in it? Probably not. I'll spend very little money on it and keep it for a short amount of time.


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[Assistant] When I was younger, I couldn't afford a lot of the new trends, but I could afford ways of making what I already had tie into a new trend. A lot of trends are color based, so you'll know that, you may know, maybe you don't know, that every year there is a new color of the year as far as interior design goes or fashion.


[User] Please transcribe this text

[Assistant] Every year there's that one colour that everybody says, that's your standout. Everyone needs this in their closet. You may not be able to afford a new closet of that colour. Let's say for example, it's oxblood.


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[Assistant] You can't afford that, but you've got a bunch of white t-shirts that you're not really using anymore. A couple of them got a little bit dingy. And you can afford the four dollar pack of dye. You can make that oxblood shirt yourself. You can be on trend by using a little bit of crafty know-how.


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[Assistant] About two years ago, there was a trend of cropped denim jackets. They were often frayed, the collar was often ripped off, and it was left with just the stand collar and that was frayed. Instead of buying those jackets, and I saw these jackets on sale for a lot of money.


[User] Please transcribe this text

[Assistant] I created my own. I took my own denim jacket that I wasn't really wearing anymore and I ripped off the hem, I ripped off the collar and I frayed it myself. It took all of 10 minutes. That jacket was just sat in my closet. It would never have seen the light of day again most likely and I turned it into that current trend. Almost every town I know of


[User] Please transcribe this text

[Assistant] In America and anywhere else I've been has some kind of craft store. Even if it's not a dedicated craft store, they'll have a craft section in your major supermarket where they'll sell fabric paints, dyes, um, sewing kits. There's always somewhere locally that you can find whatever you need to customize your clothing.


[User] Please transcribe this text

[Assistant] Trends always find a way to come back around, whether it be 10 years later, 20 years later. With clothing, you can't really reinvent the wheel. The last person that reinvented the fashion wheel was Diane van Versenburg with her wrap dress. Since then, nothing wildly revolutionaries happened as far as style has gone. Clothes have gone. And so,


[User] Please transcribe this text

[Assistant] Trends will reappear. They'll be muddled up slightly and repurposed and made new again. But they really are just repurposed trends. They'll come back over and over again. That's fine. Just know which ones are going to work for you. And if you've worn them before, don't wear them again.


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[Assistant] Knowing which clothes of yours to keep and trends to keep.


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[Assistant] It's actually very difficult to do, and I'm still trying to master it. There's certain things that you feel like you've exhausted in your closet. If you feel that way, let them go.


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[Assistant] I'm not one for hoarding. I do like to clear out my closet as much as possible. And the main reason I do that is because somebody could really benefit from the clothes that you have. So if you're not wearing it anymore, instead of keeping it in your closet for 20 years in the hopes that that trend might come back around, somebody could actually really benefit from that clothing.


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[Assistant] Edit down, give that to charity, and then if that trend does come back around, buy it again, maybe a more accessible version.


[User] Please transcribe this text

[Assistant] You will make mistakes. That's fine. You'll look back on a picture from a year ago thinking, what the heck was I thinking? What you were thinking was you were going through an evolution, you were trying new things and you wanted to find your style. Totally fine. Totally acceptable. I have things that I've worn within the last 10 years that I look back on and think, oh, that was rough.


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[Assistant] I, but I'm glad I did it because it helped me get to where I am now with my style. Some of my ruffle or ruff looks. Okay, there was one from two years ago, a year and a half ago maybe. I loved the crossbody trend. And I'm not talking about the little satchel crossbody because I still love that. I'm talking about like the fanny pack crossbody.


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[Assistant] And now I look at it and think, what grown man steps into a room and expects to be taken seriously with a bloody honing beaker on his chest? It's ludicrous. Uhm, let's keep that for the kids. I wore it in an episode of Queer Eye. Uhm, and that wasn't wise.


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[Assistant] My 21st birthday, I thought that I was Paris Hilton. And so, I wore a Von Dutch t-shirt, a Von Dutch cap, and a Von Dutch sweatpants velour.


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[Assistant] That definitely wasn't me. That was Paris Hilton. She's a white lady. I'm a brown guy. In my early twenties also.


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[Assistant] Let's say Missy Elliott, because that's who I was channeling every time I went shopping. Again, I'm not a super awesome black lady, uhm, who's at the top of her game. I was a South Asian guy, definitely pretending to be straight.


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[Assistant] I wasn't trying to be gay at that point. All those bad moments that I look back on, I was trying to be somebody I definitely wasn't.


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[Assistant] I wouldn't say that any of these things are mistakes. It's all part of getting to the place you want to be with your style. You're testing things out. You're seeing if you can make them work. So experiment, play. If you're not making any mistakes, you're not doing it right. You've not tried hard enough. It should be playful. It should be fun. It shouldn't just be safe.


[User] Please transcribe this text

[Assistant] Certain things that I wish had never gone out of style are heels for men. Heels were actually made for men by men many, many, many, many, many decades ago. And it was just to encourage men to stand in a certain way and offer them a little more height.


[User] Please transcribe this text

[Assistant] It's turned into very, very, very high heels for women. I get that. However, a two inch heel for a man should not be unacceptable. That should be perfectly ordinary. If you want to adjust that slight bit of height and it makes you stand in a certain way, I don't see why you shouldn't.


[User] Please transcribe this text

[Assistant] And so I wish that hadn't gone out of style. I wish it hadn't become taboo for men to wear a slight heel.


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[Assistant] Uhm, something that went out of style, uhm, a while ago, but I love so much for women, is a knee-high sock. I think they look gorgeous. Clueless did a really good job of making them a thing and they became such a thing that they went out of style very, very quickly. But they look super chic with the right outfit. Uhm, knee-high boots.


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[Assistant] I like a knee high boot. I love a thigh high boot. But they've been so, so, so overdone. They're starting to fall out of favor. However, I think they're a classic. They will always be around. There's just a right way and a wrong way of doing it.


[User] Please transcribe this text

[Assistant] Some of my least favourite trends since I've been around. Uhm, velour tracksuits, never exciting. Uh, bedazzled jeans were very hot in the early 90s. If I never see them again, it'll be too soon. Uhm, square toed shoes.


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[Assistant] Don't get me wrong, I do have a couple, but they are for very certain occasions, very particular pairs of pants and I use them sparingly. They are not my everyday shoe. Please don't make them your everyday shoe. Uhm, cork wedges.


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[Assistant] Just do yourself a favor and take my advice on this one. You'll never look back and think, ooh, I'm so glad I wore those. And style does not just mean the clothing or accessories that you're putting on your body. It also includes your hairstyle.


[User] Please transcribe this text

[Assistant] That red rinse that was all the rage six years ago, that color is not your friend. It's not doing you any favors. I promise you, you're going to regret it.


[User] Please transcribe this text

[Assistant] Two neat functions, the step function and its derivative, the delta function.


[User] Please transcribe this text

[Assistant] So if I can just introduce you to those functions and show you that they are very natural inputs to a differential equation. They happen


[User] Please transcribe this text

[Assistant] Okay, so the first one is the step function, and it's, I'll call it h after its inventor, who was an engineer named Heaviside, started with an h. And the step function, let's, let me write the formula. h of t is zero for t negative.


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[Assistant] And 1 for t greater or equal to 0. Okay.


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[Assistant] And it has a jump. You could say jump function also. Jump function, step function.


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[Assistant] So the jump will happen when this is zero. Step functions jump when that's zero. And that zero acts


[User] Please transcribe this text

[Assistant] That's the complete effect of changing from t to t minus a capital T is just to shift the whole thing by capital T. Okay, so keep your eye on the


[User] Please transcribe this text

[Assistant] The standard step function, which jumps at t equals 0, jumps by 1. And take its derivative.


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[Assistant] So now that's, this is the delta function. The delta function has, runs along at zero,


[User] Please transcribe this text

[Assistant] So we don't have really that this graph of a delta function is not fully satisfactory. It's great, it's perfect for all the uninteresting boring part. But at the moment of truth, when something happens in an instant, the


[User] Please transcribe this text

[Assistant] We need to know, we need to say more. We need to say more, not just, it's infinite.


[User] Please transcribe this text

[Assistant] And that'd be the delta function there. So this is what I would use. If that was the source term in my differential equation, what would that mean? If this was the q of t in the differential equation, reflecting input at different times,


[User] Please transcribe this text

[Assistant] That, that function would say no input, except at one moment, at one instant, capital T, at that instant of time, you put one in, over in an instant.


[User] Please transcribe this text

[Assistant] Well, it's not quite zero time, but it's so close to zero time that the two are connected and then the ball takes off. And so that a simple model, a workable model, is to say it happens in zero time with a delta function. So I really want to


[User] Please transcribe this text

[Assistant] Use delta functions, and they're not difficult to use.


[User] Please transcribe this text

[Assistant] The delta function is the, sorry, the step function is the integral of the delta function, right?


[User] Please transcribe this text

[Assistant] We're going in the opposite direction. We take derivatives, we get craziness.


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[Assistant] If we take integrals to go from delta, so the integral of the delta is the step function, and that's really how you know a delta function. That's the math way to describe more exactly than this arrow that just fires off.


[User] Please transcribe this text

[Assistant] What the delta function's doing. So the key property of the delta function is to know what its integral is. The integral of the delta function.


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[Assistant] Over, let's say, started, time could have started even at minus infinity, and it could go on forever to plus infinity.


[User] Please transcribe this text

[Assistant] H of t evaluated between t equal minus infinity and plus infinity, because those are the limits of integration, and what do I get?


[User] Please transcribe this text

[Assistant] At plus infinity, the step function is one. This is zero. So I get one. And everybody...


[User] Please transcribe this text

[Assistant] Catches on to that key fact that the total integral of the delta function is 1.


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[Assistant] Again, you only made the deposit at one moment, but that deposit was a full dollar and that


[User] Please transcribe this text

[Assistant] Adding up all deposits is just that one dollar.


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[Assistant] So that's the, that's the integral of the delta function.


[User] Please transcribe this text

[Assistant] Now actually, to use delta functions, I need to give you a slight generalization of that. So can I?


[User] Please transcribe this text

[Assistant] We don't like to take their derivative. The derivative of a delta function is a truly crazy function.


[User] Please transcribe this text

[Assistant] Shoots up to infinity and then it shoots down to minus infinity, the slope of that, of that arrow. But, uh,


[User] Please transcribe this text

[Assistant] It's, it's integrals that we want. So now let me integrate from minus infinity to infinity, my delta function.


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[Assistant] Times any other function. Say f of t, dt.


[User] Please transcribe this text

[Assistant] Delta is doing everything at one moment at t equals zero.


[User] Please transcribe this text

[Assistant] At that moment, t equals zero. At that moment, when t is zero, and that's the only place any action is happening, f of t is f of zero. It's whatever value it has at that point t equals zero. And that's the answer. f of zero.


[User] Please transcribe this text

[Assistant] So if f of t was the constant function 1,


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[Assistant] Then we're back to our integral up there. If that's just 1, I'm integrating delta of t, my function is 1, I get 1. But if that function is, well suppose that function is sine t.


[User] Please transcribe this text

[Assistant] What's the integral of delta of t times sine t dt? Well, sine t...


[User] Please transcribe this text

[Assistant] So the integral of delta of t sine t is sine of zero is zero.


[User] Please transcribe this text

[Assistant] Turned on, but the other term turned off. So the, nothing happened altogether. Whereas the integral of delta t e to the t, yea, tell me that one. The integral of delta t e to the t dt.


[User] Please transcribe this text

[Assistant] Well, e to the t is doing all sorts of stuff for all time, but the delta function is zero all that time.


[User] Please transcribe this text

[Assistant] One, because at that moment, t equals zero, the only important moment would be, uh,


[User] Please transcribe this text

[Assistant] e to the t function is e to the zero and it's just one. Let me ask you for another example. The integral of minus infinity to infinity of delta, let me use the shifted delta, e to the t dt. Can you compute that integral? Well again, that function is zero almost all the time.


[User] Please transcribe this text

[Assistant] The only time that impulse, the moment that impulse hits is t equal capital T. At that moment,


[User] Please transcribe this text

[Assistant] This is equal to e to the capital T and that's all that matters. Okay. So, uh,


[User] Please transcribe this text

[Assistant] So now let me use the delta function as the source term in our differential equation. So we're seeing one last time, one more, I still call it a nice function.


[User] Please transcribe this text

[Assistant] Even though it's not legitimately a function at all, the delta, but let me solve the equation dy dt.


[User] Please transcribe this text

[Assistant] Plus the delta function turned on at capital T. And let me start it from zero.


[User] Please transcribe this text

[Assistant] I don't make any deposit at all, except at one moment, t equal capital T, and in that moment, I deposit a dollar.


[User] Please transcribe this text

[Assistant] Okay, so we know what the solution is. From a deposit of one dollar.


[User] Please transcribe this text

[Assistant] And at capital T, time T, in goes the dollar, and it grows.


[User] Please transcribe this text

[Assistant] It grows, so that it grows to


[User] Please transcribe this text

[Assistant] Over the remaining time, e to the t minus capital T,


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[Assistant] For, this is for T larger than T.


[User] Please transcribe this text

[Assistant] When T at, for, when T minus capital T is a year later, our dollar is worth E.


[User] Please transcribe this text

[Assistant] When t minus capital T, when it's been in there for a year,


[User] Please transcribe this text

[Assistant] Well, that was if the interest rate was 100%, you may feel that you'd be fortunate to get that. But let's suppose you do. At 100% interest, after one year, you might say, well, my money just doubled.


[User] Please transcribe this text

[Assistant] Because I got the interest equal to the original, so I got twice it. But not true, because that money went in, uh, was growing, interest was being added, compounded through the whole year, so that after one year, starting with one, you have E.


[User] Please transcribe this text

[Assistant] At, at A is 100%. Oh! Okay, my formula isn't correct here because


[User] Please transcribe this text

[Assistant] I had an A here, but then it belongs here, so let me fix that. It's E to the A.


[User] Please transcribe this text

[Assistant] That's the growth factor up to time t starting from time, the earlier time, capital T. Okay, so you see that how we were able just to write down the solution to the differential equation, even though it's, uh, entirely new.


[User] Please transcribe this text

[Assistant] Or different, or non-standard input. Uh, the, uh,


[User] Please transcribe this text

[Assistant] Other, the step function input, so we're finding here the impulse response.


[User] Please transcribe this text

[Assistant] That's a very, very important concept in engineering. The impulse response, the response to an impulse.


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[Assistant] And for second order differential equations, this is going to be, it's really the crucial function in the subject.


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[Assistant] So this is the response to, uh, to an impulse, it's the impulse response from our standard first order equation that we've been dealing with.


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[Assistant] Now we've got, just to remember, one more step is still linear would be to allow the interest rate to change. That's one lecture, the next one. And then we get non-linear equation. So that's what's coming.


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[Assistant] Here's delta functions for the first time and not for the last time. Thank you.


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[Assistant] The dy dt is ay, that's the interest rate growing in the, in the, in the bank example. y is our total balance and q of t is our deposits or withdrawals. Only one change.


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[Assistant] Likes these integrating factors. And I call, I'll call it M.


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[Assistant] With a minus sign. dm dt equals minus a of tm. No source term, we can solve that equation.


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[Assistant] In case A is varying, we can still solve this equation. It will still be


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[Assistant] An exponential of minus something. But what we have to put here


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[Assistant] A of t dt, just to make the notation look right. Okay.


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[Assistant] And it's that a that I want. Now, why do I want this m? How does it work? Here's the reason m succeeds. Look at the derivative of m times y.


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[Assistant] Suppose A of t, instead of being constant, is growing.


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[Assistant] Then, uh, growth is going to be faster and faster as time goes on.


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[Assistant] Different from T, just to keep things straight. Okay.


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[Assistant] It's the exponential of zero in our, in our formulas for m. m of zero is one. That's where m starts. So m of zero is one. I can remove that. Okay. And now,


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[Assistant] And now if I divide by m, I have my answer. So those are the steps. Find the integrating factor.


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[Assistant] Who's integral, I just have to integrate, and then


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[Assistant] As there's minus sign in the exponent, 1 over m will have a plus sign.


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[Assistant] M here has e to the minus t squared. One over M will be e to the plus t squared.


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[Assistant] I get y of t, this will be 1 over m, that will be e to the plus the integral of a of t dt, y of 0.


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[Assistant] That's the null solution, that's the solution that's growing out of Y of zero.


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[Assistant] So, uh, and that's e to the plus the integral from 0 to s of a.


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[Assistant] And I have an M there. Ooh, wait a minute, I haven't got it right here. So I want to know what is M?


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[Assistant] At f at time s divided by m at time t.


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[Assistant] The rule for exponents is, if I have a product of two exponentials, I add the exponents. When I add this to this,


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[Assistant] This knocks off the lower half of the integral. I'm left with the integral from s to t of a. So this was an integral of a.


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[Assistant] When a is equal to 2t, this was the example, a equal to 2t.


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[Assistant] Instead of e to the a t minus s, I now have t squared minus s squared because I had an integral of a of t and a is not constant anymore. This is my example.


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[Assistant] Uh, this was an integral from zero to t, so that would be, this part would be e to the t squared.


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[Assistant] The growth factor that multiplies the later deposit is e to the t squared minus s squared and we have a


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[Assistant] So when we add those up, we get that, that sum.


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[Assistant] Ooh. Ooh. First duck, you say? Tell you what, I'll go to your secret place if you take diving lessons. You'll be studying with the master. What master? Ha ha! Oh boy, that's funny. What master? As if you didn't know. You're a funny bird, Chirp. Very funny bird.


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[Assistant] Never fear, when it comes to secrets. You can always trust a doctor.


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[Assistant] Alright, that's enough excitement. Run along now, okay? And remember, hush hush.


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[Assistant] Flower diving? Ooh, good one, Peep. See, we bunch up all the flowers like this. Like that, that's nice. And make it nice and soft and perfect for diving.


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[Assistant] Uh huh. Okay, back to listening to me.


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[Assistant] Now you've got to stick the landing or the judges will take points off.


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[Assistant] It's pretty common for people around here to drink a lot of pop. Mainly it's Mountain Dew and Pepsi.


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[Assistant] My eighteenth birthday is in eight days and, uh, I mean, people look down upon me because of my teeth. As I was a kid, I was never worried about my teeth.


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[Assistant] And how old do you reckon you were when you had your first mountain juice? Like how old? I would probably say two or three. And how much a day would you say you had?


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[Assistant] I would say at least four or five bottles. If it was cans, I would say at least a twelve pack. Twelve cans a day.


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[Assistant] I would say about six or seven cans a day. And, uh, he's only three years old.


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[Assistant] What, how does he, does he drink it from the can? No, from the bottle. She puts it in his bottle.


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[Assistant] This is a picture of Quack and Chirp being very still. And this is the real Quack and Chirp being very still.


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[Assistant] So she and Peep decided to make one pile of eight hats. And another. And then they ran out of hats.


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[Assistant] Despite all the chaos, the showing went great, and like I said, everybody was very happy.


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[Assistant] Yeah, for the reception I was the second shooter. It was a lot of fun. The reception area was very crowded as you may be able to tell by all the footage that we have. We had


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[Assistant] Not that many guests, but because it was so crowded, we had to get flexible in terms of our blocking and movement, uhm, throughout the space.


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[Assistant] Everybody was very happy when they actually saw the presentation at the end of the night and I think our mother-of-the-bride shed some tears. That was a great moment.


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[Assistant] One, two, three. If you like good music, if you want a treat.


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[Assistant] Second come the butterflies with accordions.


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[Assistant] There come the cockroaches playing saxophones.


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[Assistant] This come the fireflies with brass trumpets to toot.


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[Assistant] Six-combie army and baring tiny glutes.


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[Assistant] Seventh come the ladybugs strumming their guitars.


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[Assistant] Or maybe you're the one who's not a duck. You have pink feathers. Everyone knows that duck feathers are blue.


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[Assistant] Are you going to sleep there? Because that's where I like to sleep. Oh? I didn't know that.


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[Assistant] I agree. The world isn't big enough for two ducks named Quack.


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[Assistant] I'm just as powerful as he is. Maybe he should bow before me.


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[Assistant] How dare you interrupt my- It's okay.


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[Assistant] No longer will our people suffer or treat each other badly.


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[Assistant] From now on, I will think of you as my brother. You will be called the Tang Monk. Thank you your majesty.


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[Assistant] Journey to the West, Chapter 15, Tea with a Dragon.


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[Assistant] The Tang monk looked at the robbers. He was shaking. I'm sorry, he said, but we're just monks. We don't have any money.


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[Assistant] Wukong approached the men. They all laughed.


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[Assistant] Said one of them. Wukong laughed too.


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[Assistant] His iron bar grew, and his eyes flashed red with anger.


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[Assistant] Cried another. The robbers tripped over one another, trying to get away.


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[Assistant] Wukong raise the iron bar, ready to strike.


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[Assistant] The Tang monk sighed and then continued his journey.


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[Assistant] Said the Tang monk. Don't you have anyone with you? Asked the woman. You can't go there alone.


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[Assistant] Your companion will come back, said the woman.


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[Assistant] The old woman whispered a magical spell to the Tang monk.


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[Assistant] Cried the Tang Monk. He got down from his horse and bowed.


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[Assistant] Meanwhile, Wukong sat in the palace of the Dragon King of the Eastern Sea. He and the Dragon King were drinking tea.


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[Assistant] Wukong folded his arms and looked at the ground. The Dragon King continued.


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[Assistant] Journey to the West, Chapter 14, A Promise to Protect.


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[Assistant] The paper floated up and then disappeared among the clouds. The monk hurried back down the mountain.


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[Assistant] Said Wukong. The monk took another step back.


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[Assistant] Wukong stood under the mountain, holding it up with his hands.


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[Assistant] The Tang monk rode the horse as Wukong walked. The monkey told the monk about himself.


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[Assistant] Wukong changed into a snake, a vulture, and then back into himself.


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[Assistant] And I can become tiny, said Wukong.


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[Assistant] Journey to the West, Chapter 10, The Powerful Sage.


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[Assistant] Erlang blocked the bar with his sword and then struck back.


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[Assistant] Wukong jumped onto a cloud to get out of the way. Erlang leaped into the air.


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[Assistant] The clouds swirled and wind blew as the two giants fought in the sky. Their weapons banged together all through the night.


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[Assistant] He turned himself into a sparrow and perched on a branch.


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[Assistant] He turned himself into a fish and swam in the water.


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[Assistant] But then, a crane flew over the stream. The crane swooped down at the water. Its mouth was wide open. Wukong shot out of the stream.


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[Assistant] Wukong's eyes became windows and his mouth became a door. He turned his tail into a flagpole. A moment later, Erlang came down the hill. When he saw the temple, he scratched his head.


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[Assistant] Up in heaven, the Jade Emperor, the Queen, and Guan Yin watch the chase.


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[Assistant] Said Lausa. He took a metal ring off his arm.


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[Assistant] The monkey looked dizzy for a moment, and then fell to the ground.


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[Assistant] Hi David. I haven't seen you in class for almost two weeks. We thought you had disappeared on holiday early or something.


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[Assistant] Oh yeaah. There've been so many viruses going around this winter. The weather's been so awful for the last few weeks.


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[Assistant] Now what a complete catastrophe! Is the laptop still under warranty? If it is, then you can easily send it back to the manufacturer, and they'll send you a brand new one for free! Surely!


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[Assistant] Listen, I have the number of a really good affordable computer repair shop at home.


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[Assistant] My dad has used this guy before and he can work miracles. Let's go back to my house and we can call the repair shop and you can have some tea and cookies too.


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[Assistant] Questions 1 to 4 are based on the conversation you have just heard. Question 1.


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[Assistant] What did Sarah think David was doing for the last two weeks?


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[Assistant] What happened to David on his way back from the hospital?


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[Assistant] What does Sarah say they should do with a damaged computer?


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[Assistant] Question 4. What does Sarah say she is going to do?


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[Assistant] Thanks for having me, John. I'm so excited to talk about my latest book, which was published last month.


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[Assistant] I'd say it's a major departure, as it's not just a work of fiction. It's set 200 years in the future.


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[Assistant] Well, after years of researching soldiers and chronicling their lives during battle, I just started wondering about other facets of their lives, especially their personal lives.


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[Assistant] Yes, that focus came about when I still intended to write another book of history. I started by researching soldiers' actual personal lives, studying their letters home.


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[Assistant] Well, I realized that the historical record was incomplete, so I'd either have to leave a lot of gaps or make a lot more assumptions than a historian should.


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[Assistant] I felt too constrained, working with the past, like what I wrote needed to be fact as opposed to fiction.


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[Assistant] But writing about the future gave me more freedom to imagine.


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[Assistant] Questions 5 to 8 are based on the conversation you have just heard. Question 5. What does the man say about the woman?


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[Assistant] What does the woman say about her newly published book?


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[Assistant] What did the woman do before writing her new book?


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[Assistant] What does the woman say about her writing history books?


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[Assistant] Whether it's in the hands of animated polar bears or Santa Claus, there's one thing you'll find in nearly all ads for Coca-Cola. The characteristic glass bottle.


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[Assistant] Most Americans don't drink soda out of the glass bottles seen in Coke's ads anymore.


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[Assistant] But this week, the company is celebrating a century of the bottle that's been sold in more than 200 countries. Flashback to 1915.


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[Assistant] When a bottle of Coca-Cola costs just a nickel.


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[Assistant] As the soft drink gained in popularity, it faced a growing number of competitors.


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[Assistant] Counterfeits even trying to copy Coke's logo.


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[Assistant] So according to Coca-Cola historian Ted Ryan, the company decided to come up with packaging that couldn't be duplicated. A product request was sent to eight different glassmakers.


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[Assistant] Workers at the Rouge Glass Company got the request and began flipping through the encyclopedia at the local library, Landigang Cocoa Seed.


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[Assistant] The cocoa seed is not an ingredient of the soda.


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[Assistant] They designed their bottle based on the seed's shape and large middle.


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[Assistant] It won over Coke executives in Atlanta and would go on to receive its own trademark.


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[Assistant] Spur collections and earn Coca-Cola an iconic image that made it part of American culture for a century.


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[Assistant] It was 100 years ago this week that the bottle earned a patent.


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[Assistant] By World War II, Coke bottle sales had ballooned into billions.


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[Assistant] Americans mostly consume coke out of aluminum or plastic today.


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[Assistant] But the glass bottle remains a symbol of America that's readily recognized around the world.


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[Assistant] Questions 12 to 15 are based on the passage you have just heard. Question 12.


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[Assistant] What does research show about a conversation between strangers?


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[Assistant] What prevents people from starting a conversation with strangers?


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[Assistant] Why does a negative encounter with strangers stick in one's memory?


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[Assistant] What does the passage say the pleasure of connection seems to be?


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[Assistant] The Caribbean islands are divided into two worlds, a rich one and a poor one.


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[Assistant] This tropical region's economy is based mainly on farming. Farmers are of two types. One is the plantation owner, who may have hundreds of thousands of acres.


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[Assistant] In contrast, the small cultivator is working only a few acres of land.


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[Assistant] Most visitors to the Caribbean are rich, like the plantation owner. They do not realize or do not want to realize.


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[Assistant] That many farm families barely manage to get by on what they grow.


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[Assistant] The Caribbean produces many things. Sugar is the main product. Other export crops are tobacco, coffee, bananas, spices and citrus fruits, such as orange, lemon or grapefruit. From the West Indies also come oil, mineral pitch and many forest products.


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[Assistant] Jamaica's aluminum ore supplies are the world's largest. Oil comes from Trinidad, Aruba, and Caracas.


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[Assistant] But for many of the smaller islands, sugar is the only export. Rum, a strong alcoholic drink


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[Assistant] Which is distilled from sugar cane is also an export. The world's best rum comes from this area. Local kinds vary.


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[Assistant] From the light rums of Puerto Rico to the heavier darker rums of Barbados and Jamaica.


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[Assistant] American tourists enjoy stocking up on inexpensive, high quality Caribbean rum while they are on vacation.


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[Assistant] In Karakal, the well-known liquor of that name.


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[Assistant] Is made from the thick outer skin of a native orange.


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[Assistant] Ever since America's colonial days, the Caribbean islands have been favorite places to visit.


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[Assistant] Since World War II, tourism has increased rapidly. Because great numbers of people go there, the islanders have built elaborate resorts, developed harbors and airfields,


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[Assistant] Improved beaches and have expanded sea and air routes. Everything is at the resort.


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[Assistant] The vacationer never has any reason to explore the island.


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[Assistant] As in most places, those who have money live well indeed.


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[Assistant] Those who don't have money live at various levels of poverty.


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[Assistant] But here, the poor greatly outnumber the wealthy.


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[Assistant] A visitor will find rich people living in apartments or Spanish houses at the seaside or in the countryside. Their servants might include a cook, a maid and a nurse for the children. Most of the people live well below the poverty level.


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[Assistant] In towns, they live crowded together in tiny houses.


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[Assistant] Islanders make the best they can of what they have.


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[Assistant] Their homes are quite shabby. Sadly, most tourists never see this side of the Caribbean.


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[Assistant] Questions 19 to 21 are based on the recording you have just heard. Question 19 What will happen to children if they always get immediate satisfaction?


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[Assistant] What may prevent parents from raising confident and capable children?


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[Assistant] Why should children be encouraged to keep trying when they fail?


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[Assistant] Recording 3. It's not hard to mess up an interview.


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[Assistant] Most people feel nervous sitting across from a hiring manager.


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[Assistant] Answering questions that effectively open themselves up for judgment.


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[Assistant] Raises concerns that you might be difficult to manage.


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[Assistant] Or you might be someone that blames management for your own poor performance.


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[Assistant] Don't say that you've moved around in jobs because you haven't found the right fit or feel that you were not challenged enough.


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[Assistant] Statements like these will make you sound aimless and lost. An interviewer may well think, why would this role be any different for you? You will probably leave here in six months.


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[Assistant] It also begs the question of what type of relationship you had with your manager.


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[Assistant] It doesn't sound like you had open communication with him or her.


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[Assistant] Managers usually love people who can self sustain and enable growth through taking initiative, who are strong at following through their work, and who bring ideas and solutions to the table. If you were in a management or leadership position,


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[Assistant] When discussing your current role, never take all the credit for accomplishments or achievements.


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[Assistant] Emphasize your team and how, through their talents, your vision was realized.


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[Assistant] Most successful leaders know that they are only as good as their team.


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[Assistant] And acknowledging this in an interview will go a long way towards suggesting that you might be the right person for the position you are applying for.


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[Assistant] Lastly, have a good idea of what your role will be.


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[Assistant] And try and convey the idea that you're flexible.


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[Assistant] Asking what your role will be suggests you will limit yourself purely to what is expected of you.


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[Assistant] In reality, your role is whatever you make of it.


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[Assistant] This is especially true in small companies, where the ability to adapt and take on new responsibilities is highly valued.


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[Assistant] And this is equally important if you are just starting out.


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[Assistant] Entry level interviewees would do well to demonstrate a broad set of skills in most interviews. It's important to have a wide skill set, as many startups and small companies are moving really fast.


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[Assistant] Employers are looking for candidates that are intelligent and can quickly adapt and excel in a growing company.


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[Assistant] Do you think you can smack your tail without speeding up or slowing down? Sure! I do that all the time and stuff! What?


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[Assistant] Great! Quack! Pretend you're underwater and hold your breath. Peep and I will sing the song.


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[Assistant] Okay, we're looking for something that doesn't speed up, even if it gets an itch.


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[Assistant] You can stay underwater exactly one song long. No more, no less. Sorry, you are not turning into a fish.


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[Assistant] Peep, that's totally impossible. Ducks are webfooted pond dwellers, and fish are... fish. Do you understand? Sort of.


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[Assistant] Okay, uh, this is a good time to do two by two matrices, their eigenvalues and their stability.


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[Assistant] Two by two eigenvalues are easy, the easiest to do, easiest to understand.


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[Assistant] Good to separate out the 2x2 case from the later nxn eigenvalue problem.


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[Assistant] And eigenvectors. We're looking for a vector x.


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[Assistant] And a number lambda, the eigenvalue, so that Ax is lambda x. In other words, when I multiply by A,


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[Assistant] By a factor lambda, which could be positive, it could be zero, could be negative, could be complex number, it's a number though. So, that's the, that's the key equation. Let me go toward its solution. So I'm, I want to move that onto the left hand side. So I just write the same equation this way.


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[Assistant] And now I see that this matrix times the vector gives me zero.


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[Assistant] That matrix can't be invertible. If it was invertible, the only solution would be x equals zero. No good.


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[Assistant] So this matrix must be singular.


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[Assistant] Its determinant must be zero, and now we have an equation for the eigenvalue lambda. So lambda is how much we shift the matrix to make the determinant zero.


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[Assistant] We shift by lambda times the identity. Just subtract that from the diagonal. Okay, so can I begin with


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[Assistant] Very easy 2 by 2 matrix, the kind that we met first.


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[Assistant] Called the companion matrix. So we met this matrix when we had a second order equation. So I started with the equation y double prime plus b y prime plus c y equals, say, 0.


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[Assistant] So I started with one second order equation, and then I introduced y prime as a second unknown. So now I have a vector unknown, y and y prime, and then it, when I wrote the equation down,


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[Assistant] I won't repeat that. It led us to a two by two matrix.


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[Assistant] Two equations for two unknowns y and y prime. So there is a two by two matrix that we're interested in.


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[Assistant] But we really are going to be interested in all 2 by 2's. Okay, so let me take that to be my matrix A, my companion matrix. So I just want to go through the steps.


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[Assistant] And when I take the determinant of a 2 by 2 matrix, it's just that times that, which is minus lambda times minus lambda is lambda squared. This gives me a B lambda. And the other part of the determinant is this product.


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[Assistant] Minus c, but it comes with a minus sign, so it's plus c. So there's my equation.


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[Assistant] For the eigenvalues of a companion matrix. Companion matrix. And of course you see, that's exactly the same equation that we had for the exponent s. So lambda for the matrix case


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[Assistant] So that, this equation has solutions e to the st, when the matrix has the eigenvalues lambda equal s, those same s1 and s2. Alright. But now, I move on to a general two by two matrix.


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[Assistant] What are its eigenvalues? What did that, what did that equation look like for its two eigenvalues? So this will be a special case of this.


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[Assistant] Here I have a general matrix A, B, C, D. I've subtracted lambda from the diagonal. I'm taking the determinant. That will give me the two eigenvalues. Okay, let's do it.


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[Assistant] Then I have a minus lambda D and a minus lambda A. So I have an A plus a D lambda.


[User] Please transcribe this text

[Assistant] And a minus bc and all that is zero. Okay.


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[Assistant] It's a quadratic equation, second degree. A two by two matrix has two eigenvalues. The two roots of that equation. Okay, I just want to understand how, more and more and more about the connection of the roots lambda one and lambda two to the matrix A, B, C, D.


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[Assistant] If I know the 2x2 matrix, this tells me the eigenvalue.


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[Assistant] Okay, so how can I, so this will be a quadratic equation. It will have two roots and I can write the, so when I, if I factor this, this will factor into lambda minus lambda one times lambda minus lambda two.


[User] Please transcribe this text

[Assistant] And of course, if the numbers are nice, then I can see what lambda 1 and lambda 2 are.


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[Assistant] In that case, uh, I find the eigenvalues. If the numbers are not nice,


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[Assistant] Then lambda 1 and lambda 2 come from the quadratic formula, the minus b plus or minus square root of b squared minus 4ac. The quadratic formula will solve this equation, will tell me these two numbers. And if I multiply it out this way, I see lambda squared.


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[Assistant] Lambda 1 times lambda 2 equals 0. I've, here I've written


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[Assistant] The equation for the two lambdas. Here I've written the equation when I know the two lambdas. Why did I do this? I want to match this with this and see that this


[User] Please transcribe this text

[Assistant] Number, whatever it is, is the same as that number.


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[Assistant] This is just like a general fact about a quadratic equation. The sum of the roots is the


[User] Please transcribe this text

[Assistant] The minus coefficient of lambda. And then the constant term is the constant term. So lambda 1 times lambda 2.


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[Assistant] This is, these are facts about a 2x2 matrix, uh, ABCD.


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[Assistant] The sum of the eigenvalues, so this is the sum of the eigenvalues, so I'll put s, u, m to indicate that I'm looking at the sum, is that a plus d, a plus d are the numbers on the diagonal. So that's a little special.


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[Assistant] When I add the diagonal numbers, I get something called the trace of the matrix.


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[Assistant] I'm introducing a word trace. Trace is the add up down the diagonal. And that matches a plus d. And this, this one is the product.


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[Assistant] Right, so that if I write down some matrices,


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[Assistant] We could look at them immediately. Let me write down a matrix. Suppose I write down that matrix.


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[Assistant] Ah, let me, let me improve this a little. 2, 4, 4, 9. 2, 4, 4, 2 would be even easier. Sorry. Okay.


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[Assistant] I see immediately that two eigenvalues of that matrix add to four.


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[Assistant] 2 plus 2 is 4, I took the trace. The two eigenvalues of that matrix multiply to the determinant, which is 2 times 2 is 4 minus 16 minus 12. So the, so the sum here for that matrix would be 4.


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[Assistant] Add to 4 and multiply to minus 12. I think, actually, I think that they are 6.


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[Assistant] And minus 2. I think that the eigenvalues here are 6 and minus 2, because those add up to 4, the trace. And they multiply 6 times minus 2 is minus 12. That's the determinant.


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[Assistant] Two by two matrices, you have a good chance at sort of seeing exactly what happens. Now, my interest


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[Assistant] For this video is to use all this, use the eigenvalues to decide stability.


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[Assistant] Stability means that the differential equation has solutions that go to zero.


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[Assistant] And remember, the solutions are e to the st, which is the same as e to the lambda t.


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[Assistant] The s and the lambda both come from that same equation in the, in the case of a


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[Assistant] Second order equation reduced to a companion matrix. So I'm interested in


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[Assistant] When do the eigenvalues, when are the eigenvalues negative? When are the eigenvalues negative?


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[Assistant] Or if they're complex numbers, when are their real parts negative?


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[Assistant] So can we remember trace the sum, product the determinant, and answer the stability questions? So I'm ready for stability.


[User] Please transcribe this text

[Assistant] Either lambda 1 negative and lambda 2 negative, or this is in the real case.