Hello, I am trying to understand the concept of expression
vectors. Could you please check my statements and note wrong
statemtents. I have included “(?)” after sentences that I am most
in need of clarification.

A eukaryotic DNA cannot be transcribed in a bacterial host after
it is introduced after reverse transcription because it lacks a
promoter, which is not transcribed in the eukaryote. As a result,
the gene of interest (G.O.I) must be introduced into the bacterial
host in an expression vector. The expression vector has a promoter
(?) that is recognized by the bacterial RNA polymerase but
transcribing only begins when an inducing molecule is introduced by
the researchers, The inducer acts as a transcription factor that
allows the polymerase to bind to the promoter (?). This expression
vector can be integrated into the host chromosome or exist
independent of the host chromosome.