Axis Rotation to determine new points I am looking at this answer . 
https://math.stackexchange.com/a/62248/474907, but the formula 
c = cos(a); // compute trig. functions only once
s = sin(a);
xr = xt * c - yt * s;
yr = xt * s + yt * c;

differs from the wikipedia entry. So, I am a little confused, which one is correct.
$R_{z}(\theta )={\begin{bmatrix}\cos \theta &\sin \theta &0\\[3pt]-\sin \theta &\cos \theta &0\\[3pt]0&0&1\\\end{bmatrix}}$
https://en.wikipedia.org/wiki/Rotation_of_axes#Generalization_to_several_dimensions
EDIT:
AFter answer from @caverac
If not changing the axis
$\vec{new} = R_{active} * \vec{old}$
$R_{z}(active)={\begin{bmatrix}\cos \theta &-\sin \theta &0\\[3pt]\sin \theta &\cos \theta &0\\[3pt]0&0&1\\\end{bmatrix}}$
If changing the axis
$\vec{new} = R_{passive} * \vec{old}$
and 
$R_{z}(passive)={\begin{bmatrix}\cos \theta &\sin \theta &0\\[3pt]-\sin \theta &\cos \theta &0\\[3pt]0&0&1\\\end{bmatrix}}$
The angle is just negated ( clockwise or counter-clockwise ). Is my understanding correct?

That's the difference between an active and a passive transformation, in an active vectors are rotated, while in the passive the basis vectors are rotated
