Well, I know that, in order to rotate a triangle specified by three vectors in $R^2$ we just rotate each vector in the same angle, and to do this we apply the rotation matrix in 2 dimensions, but it will not exactly rotate the triangle itself, but it's position relative to the origin.
Of course, if we specify the triangle in a way that it will have its center in the origin, then it's gonna rotate around its own center. But can this be done in other way? Can we rotate a triangle in its own center, while the center itself isn't located at the origin?
Whatever your definition of "center" is, (call it $c$) subtract it from all the vertices, rotate the resulting triangle around the origin, then add $c$ back to the vertices of the resulting triangle.