Chapter 5.5, Problem 8E

In Exercises 7–12, use Example 6 to list the eigenvalues of A. In each case, the transformation x ↦ Ax is the composition of a rotation and a scaling. Give the angle φ of the rotation, where −π < φ < π, and give the scale factor r.

8. $\left[\begin{array}{cc}\sqrt{3}& 3\\ -3& \sqrt{3}\end{array}\right]$