Could someone please explain how to find the standard matrix? I have a test tomorrow and my professor wasn't very clear about this part, and the textbook isn't helping much, either. Here are a couple of practice problems my professor gave us:

Assume T is a linear transformation. Find the standard matrix of T.

(1.) T:R^2 -->R^2 rotates points (about the origin) through -(pi)/4 radians (clockwise)

(2.) T:R^2 -->R^2 is a vertical shear transformation that maps e1 into (e1 - 2(e2)) but leaves vector e2 unchanged.

Any help would be greatly appreciated.