The Same Point in Different Frames
Given our framework, some rather difficult
problems become easy to solve. For instance, suppose
you have 2 frames, and you know the coordinates of a
particular point relative to one of them. How would
you go about computing the coordinate of your point
relative to the other frame?
Suppose that my two frames are related by the
transform S as shown below.
Thus, the coordinate for the point in the second frame
is simply:
Even harder problems become simple. Suppose that
you want to rotate the points describing some object
(say a child) about some arbitrary axis in space (say
a merry-go-round). This is easy so long as we have the
transform relating our two frames.
 Thus, 
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