  Powering the 10^62 erg nuclear outburst in the MS0735.6+7421 cluster central
galaxy by accretion implies that its supermassive black hole (SMBH) grew by
~6x10^8 solar masses over the past 100 Myr. We place upper limits on the amount
of cold gas and star formation near the nucleus of <10^9 solar masses and <2
solar masses per year, respectively. These limits imply that an implausibly
large fraction of the preexisting cold gas in the bulge must have been consumed
by its SMBH at the rate of ~3-5 solar masses per year while leaving no trace of
star formation. Such a high accretion rate would be difficult to maintain by
stellar accretion or the Bondi mechanism, unless the black hole mass approaches
10^11 solar masses. Its feeble nuclear luminosities in the UV, I, and X-ray
bands compared to its enormous mechanical power are inconsistent with rapid
accretion onto a ~5x10^9 solar mass black hole. We suggest instead that the AGN
outburst is powered by a rapidly-spinning black hole. A maximally-spinning,
10^9 solar mass black hole contains enough rotational energy, ~10^62 erg, to
quench a cooling flow over its lifetime and to contribute significantly to the
excess entropy found in the hot atmospheres of groups and clusters. Two modes
of AGN feedback may be quenching star formation in elliptical galaxies centered
in cooling halos at late times. An accretion mode that operates in gas-rich
systems, and a spin mode operating at modest accretion rates. The spin
conjecture may be avoided in MS0735 by appealing to Bondi accretion onto a
central black hole whose mass greatly exceeds 10^10 solar mass. The host
galaxy's unusually large, 3.8 kpc stellar core radius (light deficit) may
witness the presence of an ultramassive black hole.
