Answer
$$\cos \theta=0 $$ that is, $\theta=\frac{\pi}{2}$.
Work Step by Step
Let $u=(2,2),\quad v=(-3,3), \quad =u\cdot v $.
The angle $\theta$ between $u$ and $v$ is given by the formula
$$\cos \theta=\frac{\langle u, v\rangle}{\|u\| \cdot\|v\|}=\frac{-6+6}{\sqrt{ 4+4}\sqrt{ 9+9}}=0 $$ that is, $\theta=\frac{\pi}{2}$.
