Answer
$7.13^{\circ}$
Work Step by Step
We know that the angle between two vectors is:
$\theta =\cos^{-1} [ \dfrac{u \cdot v}{||u|| \space ||v|| }]$
Therefore, $||u||=\sqrt{2^2+(-3)^2}=\sqrt{13}$ and $||v||=\sqrt{1^2+(-2)^2}=\sqrt 5$
$\theta =\cos^{-1} [ \dfrac{(2)(1)+(-3)(-2)}{ \sqrt {13}\sqrt 5}]=\cos^{-1}[\dfrac{8}{\sqrt 5 \sqrt{13}}]$
So, $\theta =7.13^{\circ}$
