function [xx yy] = rotate(x, y, th)
% rotate the x and y vectors

mat = [cos(th) -sin(th); sin(th) cos(th)];

for i = 1:length(x)
    xp(1) = x(i);
    xp(2) = y(i);
    xr = mat * xp';
    xx(i) = xr(1);
    yy(i) = xr(2);
end