2D rotation of point about origin I'm in the process of learning game development and have a question regarding a simple rotation. So far, I'm visualizing the rotation as such:

I've read this similar question but I'm struggling to understand how to apply this given formula:
$$
\begin{bmatrix}
x' \\ y'
\end{bmatrix} =
\begin{bmatrix}
\cos{\theta} & -\sin{\theta} \\
\sin{\theta} & \cos{\theta}
\end{bmatrix}
\begin{bmatrix}
x \\ y
\end{bmatrix}
$$
Given a point of $(2,3)$, what would the point be after a rotation in the $xy$ plane about the origin through an angle of $-180$ degrees?
$$
\begin{bmatrix}
x' \\ y'
\end{bmatrix} =
\begin{bmatrix}
\cos{-180} & -\sin{-180} \\
\sin{-180} & \cos{-180}
\end{bmatrix}
\begin{bmatrix}
2 \\ 3
\end{bmatrix}
$$
Is this correct?
 A: The difficulty you seem to be having is with matrix multiplication.  I suggest that you watch the Khan Academy videos on this, as he does a great job of explaining it.
For your example, we apply this as follows:
$$\left[\begin{matrix}
x' \\ y'
\end{matrix}\right]
=
\left[\begin{matrix}
\cos\theta & -\sin\theta \\
\sin\theta & \cos\theta
\end{matrix}\right]
\left[\begin{matrix}
x \\ y
\end{matrix}\right]
$$
$$\left[\begin{matrix}
x' \\ y'
\end{matrix}\right]
=
\left[\begin{matrix}
\cos180& -\sin180\\
\sin180& \cos180
\end{matrix}\right]
\left[\begin{matrix}
2 \\ 3
\end{matrix}\right]
$$
$$\left[\begin{matrix}
x' \\ y'
\end{matrix}\right]
=
\left[\begin{matrix}
-1 & 0\\
0& -1
\end{matrix}\right]
\left[\begin{matrix}
2 \\ 3
\end{matrix}\right]
$$
$$\left[\begin{matrix}
x' \\ y'
\end{matrix}\right]
=
\left[\begin{matrix}
(-1)(2)+ (0)(3)\\
(0)(2) + (-1)(3)
\end{matrix}\right]
$$
$$\left[\begin{matrix}
x' \\ y'
\end{matrix}\right]
=
\left[\begin{matrix}
-2 \\ -3
\end{matrix}\right]
$$
So, a rotation of $180$ degrees results in a new point of $(-2, -3)$.
