A. the structure of [no3]- is either trigonal planar or trigonal pyramidal draw both possible structures and determine the point group for each using drawing software. b. which irreducible representations represent the translational and rotational modes for each possible structure of [no3]-?

Look at the picture.

Explanation:

For planar anion point group is D3h. For trigonal piramidal point group is C3v.

On picture 2 and 3 are the tables for each point group. Irreducible representations its the horizontal rows in tables. Where you see x, y and z it's translation of p-orbitals. Where you see R - it's rotations.

the answer is   c.) 1575 j.

explanation: