# Arrow[] moving on its own, from the wrong spot

I'm trying to animate a rotating arrow within a plot, and I'm seeing two issues I can't figure out how to resolve.

1) The arrow isn't originating from {0,0} as I have demanded.

2) The length of the arrow is changing as it rotates.

Animate[
w0 = 1 - t;
θ = π/2 - t π/2;
Plot[{t, -t}, {z, -10, 10}, PlotRange -> {{-10, 10}, {-2, 2}},
PlotStyle -> {Black, Black}, ImageSize -> Large,
Epilog ->
Arrow[{{0, 0}, {Cos[θ], Sin[θ]}}]}]]], {t, 0, 1}]


If I try to set the origin of the arrow instead to Scaled[{0,0}], the arrow doesn't rotate (and is still in the wrong place) unless I also scale the destination. Doing both of these, the arrow rotates but still not from the origin of the plotspace. Further, this is a problematic method since I also want to stretch the arrow (at the endpoint) as the animation runs further (excluded in the MWE).

Edit: MMA 11.3

Don't use Inset, since that disconnects the coordinates of the Arrow from the coordinates of the Plot:

Animate[
w0 = 1-t;
θ = π/2-t π/2;
Plot[
{t,-t},
{z,-10,10},
PlotRange->{{-10,10},{-2,2}},
PlotStyle->{Black,Black},
ImageSize->Large,