Answer
$$\cos \theta=\frac{-1}{\sqrt 2}$$
That is, $\theta = 135^o$
Work Step by Step
Let $u=(1,-1),\quad v=(0,1), \quad =u\cdot v $.
The angle $\theta$ between $u$ and $v$ is given by the formula
$$\cos \theta=\frac{\langle u,v\rangle}{\|u\| \cdot\|v\|}=\frac{0-1}{\sqrt{ 1+1}\sqrt{ 0+1}}=\frac{-1}{\sqrt 2}$$
That is, $\theta = 135^o$
