Learn Russian: Это домашняя работа.

When you are pointing something out and saying 'This is a...', you always use the fixed word Это, regardless of the noun's gender. You would only use the feminine Эта if it was directly attached to the noun to describe it, like in Эта домашняя работа... (This homework...).

Most feminine adjectives end in -ая. Why does домашняя end in -яя?

The dictionary form of this adjective is домашний (home/domestic). It belongs to a group of soft-stem adjectives. Because of this, it takes the soft feminine ending -яя instead of the standard hard ending -ая.

Since we are learning the genitive plural, how would the adjective домашняя change if we used it in that case?

It would become домашних. Because домашний is a soft-stem adjective, it takes the soft -их ending rather than the hard -ых ending. For example, if you wanted to say 'a lot of homework assignments', you would use the genitive plural: много домашних работ.