What is the good way to remember the signs of the rotational matrix? Recall rotational matrix in (x,y) is given by:
$R =  \begin{bmatrix}  \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{bmatrix}$
For the life of me I cannot remember if the top right sin entry has a negative or positive sign, and I have known this matrix since 5 years ago (obviously I am a failure!!).
Sure one could always derive from first principle via:

But if someone just went up to you and asked you to write down the matrix, what is a good way in the least time write down the matrix and verify that it is correct (with the correct signs)?
 A: Use complex numbers.
To rotate $x + iy$ through an angle $\theta$, multiply by
$e^{i\theta} = \cos \theta + i \sin \theta$
$(x + iy)(\cos \theta + i \sin \theta) =
(x \cos \theta - y \sin \theta) + i(x \sin \theta + y \cos \theta)$
which corresponds to
\begin{pmatrix}
   \cos \theta & -\sin \theta\\
   \sin \theta & \cos \theta
\end{pmatrix}
Practically, all you really need to figure out is that the real part is
$x \cos \theta - y \sin \theta$, or that the imaginary part is
$x \sin \theta + y \cos \theta$.
I just remember that the signs in the top row are $1^2$ and $i^2$.
A: Take $\theta=\pi/2$, and write down one of the options. It is fairly easy to check in this case whether you got a clockwise or anti-clockwise rotation.
A: My idea is similar to Steven's.
Write complex numbers in vector forms on the complex plane.
Rotating $\begin{pmatrix} \cos{\gamma}\\\sin{\gamma}\end{pmatrix}$ through angle $\theta$ counterclockwise, 
it is located at $\begin{pmatrix} \cos{(\gamma+\theta)}\\\sin{(\gamma+\theta)}\end{pmatrix}$.
By the Trigonometric Addition Formulas, 
$$\cos{(\gamma+\theta)}=\cos{\gamma}\cos{\theta}-\sin{\gamma}\sin{\theta},$$
$$\sin{(\gamma+\theta)}=\sin{\theta}\cos{\gamma}+\sin{\gamma}\cos{\theta},$$
you can know the matrix $A$ which satisfies 
$$A
\begin{pmatrix} \cos{\gamma}\\\sin{\gamma}\end{pmatrix}
=
\begin{pmatrix} \cos{(\gamma+\theta)}\\\sin{(\gamma+\theta)}\end{pmatrix}$$
is 
$$\begin{pmatrix} \cos{\theta}& -\sin{\theta} \\ \sin{\theta}& \cos{\theta} \end{pmatrix}.$$
