well...

You can go through the lengthy process of finding the angle of (3,-2) and the angle of (2,3) and subtracting but if you just look at a quick sketch

it sure looks like there's $\pi/2$ radians between those two points.

That gets you a rotation matrix of

$R=\begin{pmatrix}0 &-1 \\1 &\phantom{-}0 \end{pmatrix}$

and checking

$R \begin {pmatrix}\phantom{-}3 \\-2\end{pmatrix} = \begin{pmatrix}2 \\ 3\end{pmatrix}$

as desired.