Let Q be an orthogonal 2 ( 2 matrix and let x and y be vectors in.

Question:

Let Q be an orthogonal 2 ( 2 matrix and let x and y be vectors in. If ( is the angle between x and y, prove that the angle between Qx and Qy is also (. (This proves that the linear transformations defined by orthogonal matrices are angle-preserving in, a fact that is true in general.)