Definition of a Tangent Plane We all have and intuitive idea of what the tangent plane to a point on a given surface should be. It is the plane that goes through that point and that it is tangent to the surface at that point. Suppose. z = f(x,y) is a smooth surface above the xy-plane (see the picture below).
The two prokaryotic domains (or empires),  Bacteria  (or  Eubacteria ) and  Archaea  (or  Archaeobacteria ), are subdivided into 35 phyla (or divisions): 30 phyla in the domain  Bacteria , and 5 phyla in the domain  Archaea .
Classifying Organisms in their Kingdoms. The Kingdom Eubacteria consists of mostly heterotrophic bacteria that come in three main shapes. They are cocci (spherical), bacilli (rod shaped-as shown above), and spirilla (corkscrew shape). This kingdom is one of the two prokaryotic kingdoms. Bacteria in this kingdom have cell walls made without peptidoglycan. It is part of the Domain Bacteria.