To my memory, on this page the lazy Admiral straight-up asks Tatsuta to sleep with him. She surprisingly agrees, with the condition that he work hard all day. He does so, only to end up so exhausted that he falls asleep the instant his head hits the pillow.
Tatsuta's characterization in this series is so wonderful, but hard to describe. She is much less trollish and sadistic than she is usually portrayed. But in exchange, she has this "heart of darkness" aspect.
For example, at one point on sortie Tenryuu is shocked to find Tatsuta covered in blood, and Tatsuta doesn't even notice it until Tenryuu points it out. Another time the Admiral tries to give her a gift but she refuses, saying she's only a weapon and could sink tomorrow.