Rotation matrix from the mean dynamical equator and equinox at J2000.0 to the ICRS

Recommendation VII of Resolution A4 of the XXIst General Assembly of the International Astronomical Union (IAU \cite{iau1992}) states, in part, ``... that the principal plane of the new conventional celestial reference system be as near as possible to the mean equator at J2000.0 and that the origin in this principal plane be as near as possible to the dynamical equinox of J2000.0, ..." The resulting International Celestial Reference System (ICRS), however, has a small, but significant, offset requiring a rotation matrix. The solutions for the offset between the mean dynamical pole of the Earth at J2000.0 and the pole of the ICRS determined by Lunar Laser Ranging (LLR) and Very Long Baseline Interferometry (VLBI) differ by several σ. Similarly, two different definitions have traditionally been used for the position of the mean equinox. Which of these poles and equinoxes should be used is application dependent. We have shown how the rotation matrix for the rotation from the mean dynamical equator and equinox at J2000.0 to the ICRS changes depending on the various assumptions made in constructing it.