While Petra may be unfamiliar with modern weaponry (the portrait behind her shows an armoured man carrying an axe and is still in its first frame), she knows when she's looking at one and the formal setting aside does a lot for her nerves. Wielding authority quite like this is still new to her, and still slightly disconcerting; she remains constantly aware of her own background and limitations. (Her attitude thus far is 'well, I have to do it anyway, so I will'.)

"For as long as I hold that authority, I'll consider you my respected equal." No, she didn't follow everything that Judith said initially in introducing herself, but she can figure out the gist of it and she vaguely recalls Judith's announcement of territory in another part of the city. It'll do, and in fairness 'respected equal' is a nice thing to say that can still cover a multitude of sins if she needs it to later. "Thank you for joining me- please, sit down."