Answer
$45^{\circ}$
Work Step by Step
$\textbf u =\langle 4,0 \rangle$
$\textbf v =\langle 2,2 \rangle$
$\cos\theta=\frac{ \textbf u . \textbf v }{ | \textbf u | | | \textbf v | } $
$\cos\theta=\frac{ \langle 4,0 \rangle . \langle 2,2 \rangle }{ | \sqrt {4^2+0^2}| | | \sqrt { 2^2+2^2} | } $
$\cos\theta=\frac{ 4\times 2+0\times 2 }{ | 4| | | {\sqrt { 8} | } }$
$\cos\theta=\frac{ 8 }{ 8\sqrt 2 }=\frac{1}{\sqrt 2} $
$\cos\theta=\frac{1}{\sqrt 2}$
$\theta=\cos^{-1}\left(\frac{1}{\sqrt 2}\right)=45^{\circ}$
