The broad energy range spanned by ASTRO-H instruments, from ~0.3 to 600 keV, with its high spectral resolution calorimeter and sensitive hard X-ray imaging, offers unique opportunities to study black holes and their environments. The ability to measure polarization is particularly novel, with potential sources including blazars, Galactic pulsars and X-ray binaries. In this White Paper, we present an overview of the synergistic instrumental capabilities and the improvements over prior missions. We also show how ASTRO-H fits into the multi-wavelength landscape. We present in more detail examples and simulations of key science ASTRO-H can achieve in a typical 100 ksec observation when data from all four instruments are combined. Specifically, we consider observations of black-hole source (Cyg X-1 and GRS 1915+105), blazars (Mrk 421 and Mrk 501), a quasar (3C 273), radio galaxies (Centaurus A and 3C 120), and active galaxies with a strong starburst (Circinus and NGC 4945). We will also address possible new discoveries expected from ASTRO-H.
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