  In the paper, we consider bivariate isotropic dilation matrices that are
similar (up to constant factors) to rotation matrices; and we show that, in
this case, the two-scale relation can be considered also as the relation
between not only dilated but also rotated scaling functions. We present
sufficient conditions on a dilation matrix to be similar to a rotation matrix,
where the similarity transformation matrix is symmetric positive definite. Also
we present a simple test that the dilation matrix performs the rotation by an
incommensurable to $\pi$ angle. We show that if a dilation matrix is similar to
a rotation matrix, then an ellipse defined by the similarity transformation
matrix is invariant (up to a homogeneous dilation) under the transformation by
the dilation matrix.
