  Clusters of galaxies are embedded in halos of optically thin, gravitationally
stratified, weakly magnetized plasma at the system's virial temperature. Due to
radiative cooling and anisotropic heat conduction, such intracluster medium
(ICM) is subject to local instabilities, which are combinations of the thermal,
magnetothermal and heat-flux-driven buoyancy instabilities. If the ICM rotates
significantly, its stability properties are substantially modified and, in
particular, also the magnetorotational instability (MRI) can play an important
role. We study simple models of rotating cool-core clusters and we demonstrate
that the MRI can be the dominant instability over significant portions of the
clusters, with possible implications for the dynamics and evolution of the cool
cores. Our results give further motivation for measuring the rotation of the
ICM with future X-ray missions such as ASTRO-H and ATHENA.
