Chapter 10.4, Problem 12PE

For Exercises 9-14, assume that the $x\text{-}$ and $y\text{-axes}$ are rotated through angle $\theta$ about the origin to form the $x\text{'}\text{-}$ and $y\text{'}\text{-axes}$ . (See Example 2)

Given $\theta ={45}^{\circ }$ and $P\left(-\sqrt{2},5\sqrt{2}\right)$ in the $x\text{'}y\text{'}\text{-plane,}$ find the coordinates of $P$ in the $xy\text{-plane}$ .