Why is this rotation "incorrect"? I've been trying to use the following formula for the rotation of a point around the origin:

$$
\begin{bmatrix}
x' \\ y'
\end{bmatrix} =
\begin{bmatrix}
\cos{\theta} &amp; -\sin{\theta} \\
\sin{\theta} &amp; \cos{\theta}
\end{bmatrix}
\begin{bmatrix}
x \\ y
\end{bmatrix}
$$

Now, I'm trying to apply this formula to the coordinate $(5,3)$ and rotating it $90$ degrees clockwise, and I ended up with the following result:

$$
\begin{bmatrix}
x' \\ y'
\end{bmatrix} =
\begin{bmatrix}
\cos{90} &amp; -\sin{90} \\
\sin{90} &amp; \cos{90}
\end{bmatrix}
\begin{bmatrix}
5 \\ 3
\end{bmatrix} 
\\
=
\begin{bmatrix}
0 &amp; -1 \\
1 &amp; 0
\end{bmatrix}
\begin{bmatrix}
5 \\ 3
\end{bmatrix} 
\\
=
\begin{bmatrix}
0(5) -1(3) \\
1(5) + 0(3)
\end{bmatrix} \\
=
\begin{bmatrix}
-3 \\ 5
\end{bmatrix}
$$

I ended up with the rotated coordinates $(-3,5)$. Unfortunately, this was wrong. Can anyone tell me what I'm doing wrong, and how I can do it correctly? I tried this method on other coordinate points, and all of them were wrong as well.
It seems right to me. Ah, maybe you're thinking of a clockwise rotation. That matrix gives a counterclockwise rotation through an angle $\theta$.
It is correct. What makes one think that it is wrong? You mean the convention that CCW is positive?

EDIT1:

What I meant is with Clockwise rotation I obtain $(-3,5)$ by matrix multiplication and Counterclockwise rotation gives  $(3,-5)$ for a diametrically opposite point. So only association with sign convention of rotation could be the source of error.