Ответ:

  1. The weather is very nice today.
  2. I am not tired.
  3. This case is very heavy.
  4. These cases are very heavy.
  5. The dog is asleep.
  6. Look! There is Carol.
  7. I am hot. Can you open the window?
  8. This castle is one thousand years old.
  9. My brother and I are good tennis players.
  10. Ann is at home but her children are at school.
  11. I am a student. My sister is an architect.

Правило: с I употребляется am, с существительным или местоимением в единственном числе — is, во множественном числе — are.