<prompt> Calculate the Cosine similarity between the following two sentences.She is the most beautiful girl in school.The girl attends the college every day.  <response>: To calculate the cosine similarity between two sentences, we need to convert those sentences into vectors using a vectorization method such as Bag of Words or TF-IDF. Then, we can take the dot product of the two vectors and divide it by the product of the magnitude of each vector.Converting the sentences into vectors using Bag of Words:Dictionary: she, is, the, most, beautiful, girl, in, school, attends, college, every, daySentence 1: 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0Sentence 2: 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1The dot product of the two vectors is 10 10 11 10 10 11 10 10 01 01 01 01 2The magnitude of vector 1 is sqrt12 12 12 12 12 12 12 12 02 02 02 02 sqrt8 2.828The magnitude of vector 2 is sqrt02 02 12 02 02 12 02 02 12 12 12 12 sqrt6 2.449The product of the magnitudes is 2.828 2.449 6.928Therefore, the cosine similarity between the two sentences is 2 6.928 0.289. 