Why is this rotation "incorrect"? I've been trying to use the following formula for the rotation of a point around the origin:
$$
\begin{bmatrix}
x' \\ y'
\end{bmatrix} =
\begin{bmatrix}
\cos{\theta} & -\sin{\theta} \\
\sin{\theta} & \cos{\theta}
\end{bmatrix}
\begin{bmatrix}
x \\ y
\end{bmatrix}
$$
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:
$$
\begin{bmatrix}
x' \\ y'
\end{bmatrix} =
\begin{bmatrix}
\cos{90} & -\sin{90} \\
\sin{90} & \cos{90}
\end{bmatrix}
\begin{bmatrix}
5 \\ 3
\end{bmatrix} 
\\
=
\begin{bmatrix}
0 & -1 \\
1 & 0
\end{bmatrix}
\begin{bmatrix}
5 \\ 3
\end{bmatrix} 
\\
=
\begin{bmatrix}
0(5) -1(3) \\
1(5) + 0(3)
\end{bmatrix} \\
=
\begin{bmatrix}
-3 \\ 5
\end{bmatrix}
$$
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.
 A: It seems right to me. Ah, maybe you're thinking of a clockwise rotation. That matrix gives a counterclockwise rotation through an angle $\theta$.
A: For future reference, or for anyone who happens to stumble upon this question looking for help, here's the two proper equations for rotation, where $\theta$ is a positive number in the range $0\rightarrow360$, and $x$ and $y$ are the $x$ and $y$ values for your point.
Clockwise
$$
\begin{bmatrix}
x' \\ y'
\end{bmatrix} =
\begin{bmatrix}
\cos{\theta} & \sin{\theta} \\
-\sin{\theta} & \cos{\theta}
\end{bmatrix}
\begin{bmatrix}
x \\ y
\end{bmatrix}
$$
Counterclockwise
$$
\begin{bmatrix}
x' \\ y'
\end{bmatrix} =
\begin{bmatrix}
\cos{\theta} & -\sin{\theta} \\
\sin{\theta} & \cos{\theta}
\end{bmatrix}
\begin{bmatrix}
x \\ y
\end{bmatrix}
$$
Alternatively, you can just use positive and negative rotation values for $\theta$ as well.
A: 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.
