Learn Russian: Кот прячется за шторой, а мышь сидит под ковром. - The cat is hiding behind the curtain, and the mouse is sitting under the rug.

The prepositions за (behind) and под (under) take the Instrumental case when answering the question 'where?' (static location). Since the cat and mouse are just staying in their locations, we use the Instrumental forms of штора (curtain) and ковёр (rug).

What happened to the spelling of ковёр (rug) in the phrase под ковром?

Ковёр is a masculine noun. To put it in the Instrumental case, we add the ending -ом. It also has a 'fleeting vowel,' meaning the ё drops out of the stem when an ending is added, changing the word from ковёр to ковром.

Why does the verb прячется (is hiding) end in -ся?

The -ся ending makes the verb reflexive. The base verb прятать means to hide an object (like hiding a toy). By adding -ся, it means the cat is doing the action to itself — it is hiding itself.

Why use the conjunction а instead of и for the word 'and' here?

А is used to show contrast or to switch focus. While и just lists things, а emphasizes that we are looking at two different subjects (a cat and a mouse) doing two different things in completely different situations.