Protractor on the dial from 180°, as the dial is graduated from opposite zero marks to 90° each way. Since the spaces, both on the main scale and the Vernier scale, are numbered both to the right and to the left from zero, any angle can be measured. The readings can be taken either to the right or to the left, according to the direction in which the zero on the main scale is moved. Reading the Vernier scale: The bevel protractor Vernier scale may have graduations of 5′ (minutes) or 1/12°. Each space on the Vernier scale is 5′ less
Semi-invariant of a quiver the coefficients of the characteristic polynomial In case Q has neither loops nor cycles the variety "k"[Rep(Q,d)] has a unique closed orbit corresponding to the unique d-dimensional semi-simple representation, therefore any invariant function is constant. Elements which are invariants with respect to the subgroup SL(d) := ∏ SL(d("i")) form a ring, SI(Q,d), with a richer structure called ring of semi-invariants. It decomposes as where A function belonging to SI(Q,d) is called semi-invariant of weight "σ". Consider the quiver Q: Fix d = ("n","n"). In this case "k"[Rep("Q",("n","n"))] is congruent to the set of square matrices of size "n": "M"("n"). The