Determine if the fixed points of the following systems are nodes, saddle points, or spirals, and determine their stability.:

(a) $${\dot x_1} = -3x_1 + \sqrt{2}x_2, \quad {\dot x_2} = \sqrt{2} x_1 - 2x_2;$$

(b) $${\dot x}_1 = x_1+x_2, \quad {\dot x}_2 = 4x_1+x_2;$$

(c) $${\dot x}_1 = -\frac{1}{2}x_1+x_2, \quad {\dot x}_2 = -x_1-\frac{1}{2}x_2.$$