Cross Ange: Tenshi to Ryuu no Rondo

Betrayed, stripped of her birthright, and declared less than human. Everything that Princess Angelise Ikaruga Misurugi of the Misurugi Empire thought she knew about her world was a lie. Now, for the crime of not being able to use magic, she’s been sentenced to certain death as a slave-soldier. The girl now known as Ange is no longer an innocent Princess: she’s learning how to kill draconic invaders, defending the same traitors who stole her life. However, they made a fatal mistake: they gave her access to an incredible weapon.

(Source: Sentai Filmworks)