Which of the following is a jet-powered, twin-engine carrier-based aircraft?

The S-3B Viking is a jet-powered, twin-engine carrier-based aircraft designed primarily for anti-submarine warfare and later adapted for other multi-role missions. Its design allows it to operate from aircraft carriers, utilizing jet propulsion for fast and efficient travel. The S-3B Viking features a unique aerodynamic design optimized for carrier operations, including the capability to conduct missions in various environmental conditions.

In contrast, the C-130 Hercules is a turboprop military transport aircraft, which does not fit the criteria of being jet-powered or carrier-based. The MH-53E Sea Dragon is a heavy-lift helicopter designed for mine countermeasures, and while capable of ship operations, it is not jet-powered nor does it operate from a carrier in the same manner as fixed-wing aircraft. The V-22 Osprey is a tiltrotor aircraft that combines elements of conventional helicopters and airplanes, but it is not classified as a jet-powered aircraft and is not specifically designed for carrier operation like the S-3B Viking.

Thus, the S-3B Viking is distinctly positioned as a jet-powered, twin-engine carrier-based aircraft, which makes it the correct choice.