Enter the military ship
The tram station offers access to the Upgrade bench as well as a container and a crate. Further on your way you will find another crate, a container and the Store. Get through the round hatch. On the other side you will find a locker with a Medium air can and another hatch.
Clear radioactive material (6/6)
The door leading to the ship is locked, because the sensors detected some radioactive materials. You will need to remove the six glowing spheres floating about the room, by tossing them into space. In order to do that you will need to stomp on each of the six fuses around the door in the center of the room, but don't do that until you place the spheres near the door - opening it will suck out all the air and put quite a pressure on you. When you destroy the last of the six fuses try to position yourself around one of the two Oxygen rechargers in the room.
Toss all the spheres out into the space and fight the appearing necromorphs. Use the Oxygen recharger when it's necessary. When you deal with the radiation jump through the round hatch and into the ship.
Find the singularity core
There's a container, right to your left, but pay close attention to the energy coming out from the floor. Use the Save station and enter the cargo area. Two more crates to smash here. Make your way through the room by moving the glowing containers along the rails - nothing very refined here.
Your way is blocked by mutated, ultrafast soldiers, they are not as tough as they may seem however. After dealing with the first wave, proceed deeper into the room. Use the kinesis to open the way to the torpedo room.
There are some containers and crates here. Get through the wide elevator door and take note of the crate to your right. Use the Save station. Calling the elevator will result in a malfunction and trigger an attack. The attempt to use the coil from the other side of the room proves futile - only after shooting the mechanism with stasis will you be able to plug the coil in. When everything's working, get into the elevator.
Head to the armoury and search the room after you deal with all the enemies. There's a crate here, as well as a Power node locker.
You can test your aim at the shooting range - you'll also find an Audio log there. Get into the infirmary, use the Stasis recharger, and enter the next room.
The lasers here ought to kill you unless you hit their source with stasis. When you do, run over to the other side of the room and deal with the attacking necromorphs. There are some crates here that you might want to check out after you slow the lasers down again. Then head to the barracks.