Chapter 1.9, Problem 26E

Let $T_A=R^2\to R^2$ be multiplication by

$A=\left[\begin{array}{l}{\cos }^2\theta -{\sin }^2\theta -2\sin \theta \cos \theta \\ 2\sin \theta \cos \theta {\cos }^2\theta -{\sin }^2\theta \end{array}\right]$

1. a. What is the geometric effect of applying this transformation to a vector x in R²?
2. b. Express the operator T_A as a composition of two linear operators on R².