  Understanding the processes that drive galaxy formation and shape the
observed properties of galaxies is one of the most interesting and challenging
frontier problems of modern astrophysics. We now know that the evolution of
galaxies is critically shaped by the energy injection from accreting
supermassive black holes (SMBHs). However, it is unclear how exactly the
physics of this feedback process affects galaxy formation and evolution. In
particular, a major challenge is unraveling how the energy released near the
SMBHs is distributed over nine orders of magnitude in distance throughout
galaxies and their immediate environments. The best place to study the impact
of SMBH feedback is in the hot atmospheres of massive galaxies, groups, and
galaxy clusters, which host the most massive black holes in the Universe, and
where we can directly image the impact of black holes on their surroundings. We
identify critical questions and potential measurements that will likely
transform our understanding of the physics of SMBH feedback and how it shapes
galaxies, through detailed measurements of (i) the thermodynamic and velocity
fluctuations in the intracluster medium (ICM) as well as (ii) the composition
of the bubbles inflated by SMBHs in the centers of galaxy clusters, and their
influence on the cluster gas and galaxy growth, using the next generation of
high spectral and spatial resolution X-ray and microwave telescopes.
