“Who gave him the 'authority' to do this?” “He didn't do it 'on his own authority' [=he didn't do it on his own]; he was acting 'under the authority of' the company president.” [=the company president gave him the power to do it]
No one 'in authority' objected to the plan. = No one 'in a position of authority' objected to the plan. [=no one with official power to make important decisions objected to the plan]
This office has 'authority' over personnel matters. [=this office has the power to make decisions about personnel matters]
(..) Yes. A mimetic polyalloy. What does that mean? Liquid metal. Where are we going? - We have to get out of the city. And avoid the authorities. I gotta stop by my house and pick up some stuff. - Negative. The T- will definitely try to reacquire you there. You sure? (..)1991 Terminator 2: Judgment Day