Scalar versus invariant in Newtonian mechanics

I looking up coriolis transport theorem for rotating refrence frames and while reading through this derivation he wrote:

In Newtonian mechanics, scalar quantities must be invariant for any given choice of frame,...

He is refering to the acceleration. I don't know the reasoning for that, but I know that it's clear for the length of the "vector from source to test point" which is scalar and invariant over transformation and rotation.

Question:

• Why is acceleration invariant over transformation and rotation?
• Why In Newtonian mechanics, must scalar quantities be invariant for any given choice of frame?
• some rigorous math read for scalar vs invariant "hopfully doesn't include tensors".
• Some history read for scalar vs invariant.
• The distance from the origin to a particular point is not invariant, since if you move the origin the distance is different. So it is probably a very limited meaning intended... – Emil Jun 16 '18 at 9:28
• I meant difference vector from source to dist. – I.Omar Jun 19 '18 at 3:47
• Scalar quantities aren't just invariant in Newtonian mechanics, they're invariant in relativistic physics too. – Mozibur Ullah Jun 19 '18 at 7:33
• not after Lorentz transformation. – I.Omar Jun 19 '18 at 11:35