There are a few ways to get accepted and receive your commission. Naval Academy, NROTC, and other programs after you are in college. All require a college degree, and as a nuclear trained officer, it is best for you to go into the Navy with a technical degree under your belt. Applications for NROTC are separate from applications for the school you want to attend, but there needs to be a unit already at your school of choice. Your options are still open after being accepted into the NROTC scholarship program. You still must decide what you want to do in the Navy. The nuclear program requires additional examinations and an interview at Naval Reactors to be personnally selected by the Admiral. After that it is two more years of college until you graduate and are commissioned. Then it's off to Nuclear Power School, Prototype trainer, and Naval Submarine School (if you choose subs) or a carrier for your first at sea duty station.
