Answer:
the third one. many people think that it is impossible to introduce a dog into a household that already has a cat.
Adverbs usually end in -ly, so Brilliantly = adverb.
Our homework is corrected by the teacher
Although the teacher is doing the action, the subject of the sentence is "our homework". It also uses a form of to be (in this case it is "is"). Both of these things are what makes a passive sentence.
Hope this helped!