The submarine is an Astute Class nuclear attack submarine. As of the time of the episode, there were only two active ships: The lead ship of the class Astute and the second ship, Ambush. It's later identified as the Achillies, which does not exist.
When Lieutenant Foster asks Ensign Mason to man the sonar station he hesitates because he has never done it before, but she tells him she knows he can do it because he passed the murder boards. In the United States military a murder board is a group of people that help a person prepare for a difficult exam, usually an exam to qualify for a position or promotion, by asking them the types of questions that might appear on the test.