During transcription, what happens to the rna polymerase of a repressive protein attaches to the operator?

If a repressive protein attaches to the operator RNA polymerase cannot attach to the promoter.

Repressor is a protein which binds to the DNA (or RNA), more precisely to the operator or associated silencers

and thus inhibits the expression of one or more genes. Its mechanism is to block the attachment of RNA polymerase to the promoter. As a result, transcription is stopped.

any abiotic or biotic factor in an ecosystem that causes a population's size to slow or decrease is a limiting factor.

i would say it is