제출해야 해요 means “must submit” or “have to submit.” The pattern verb stem + -아/어야 하다/되다 expresses obligation or necessity (“need to…”). Here:
• 제출하다 → 제출하 + 어야 하다 → 제출해야 하다
• In polite speech, 하다 → 해요, giving 제출해야 해요.
-해야 해요 is polite speech (존댓말) at the standard everyday level. To switch to a more formal or written style (격식체), you could say:
• 자료를 복사하여 교수님께 제출해야 합니다.
Here -하여 is the formal connective (instead of -해서) and -합니다 is the formal declarative.
Keep 복사해서 and turn 해야 해요 into the past 해야 했어요:
자료를 복사해서 교수님께 제출해야 했어요.
This means “I had to copy the materials and submit them to the professor.”
Use -아/어야 할 거예요 for future necessity:
자료를 복사해서 교수님께 제출해야 할 거예요.
This translates as “I’m going to have to copy the materials and submit them to the professor.”