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We present self-consistent, 3D core-collapse supernova simulations of a 40 Msun progenitor model using the isotropic diffusion source approximation for neutrino transport and an effective general relativistic potential up to $\sim0.9$~s~postbounce. We consider three different rotational speeds with initial angular velocities of $Ω_0=0$,~0.5, and~1~rad~s$^{-1}$ and investigate the impact of rotation on shock dynamics, black hole formation, and gravitational wave signals. The rapidly-rotating model undergoes an early explosion at $\sim 250$~ms postbounce and shows signs of the low $T/|W|$ instability. We do not find black hole formation in this model within $\sim 460$~ms postbounce. In contrast, we find black hole formation at 776~ms~postbounce and 936~ms~postbounce for the non-rotating and slowly-rotating models, respectively. The slowly-rotating model explodes at $\sim 650$~ms postbounce, and the subsequent fallback accretion onto the proto-neutron star (PNS) results in BH formation. In addition, the standing~accretion~shock~instability induces rotation of the proto-neutron star in the model that started with a non-rotating progenitor. Assuming conservation of specific angular momentum during black hole formation, this corresponds to a black~hole spin parameter of $a=J/M=0.046$. However, if no explosion sets in, all the angular momentum will eventually be accreted by the BH, resulting in a non-spinning BH. The successful explosion of the slowly-rotating model drastically slows down the accretion onto the PNS, allowing continued cooling and contraction that results in an extremely high gravitational-wave frequency ($f\sim3000$~Hz) at black~hole formation, while the non-rotating model generates gravitational wave signals similar to our corresponding 2D simulations.