Lagrange - The Flower of Rin-ne

As a girl named Madoka Kyono rescues a girl from drowning, she finds her school uniform missing and later returned by a strange girl. Later that night, Madoka is questioned by her sister about something. The next day, Madoka once again meets the girl, who introduces herself as Lan and asks Madoka to pilot a robotic aircraft at an offshore base. As Madoka touches the aircraft and experiences a flashback of sorts, a robot from outer space appears and attacks the base. Lan reveals herself to be an alien sent to protect Madoka and the aircraft, the two of which are linked together. Madoka agrees to pilot the aircraft, which responds to her emotions and changes into a robotic form to fight against the enemy robot, defeating it using Madoka's knowledge of club activities.