Each of the following linear system has complex eigenvalues. For eachsystem, (a) find the eigenvalues; (b) determine if the origin is a spiral sink, a spiral source, or a center; (c) determine the natural period and natural frequency of the oscillations; (d) determine the direction of the oscillations in the phase plane; and (e)using HPGSystemSolver, sketch thexy-phase portrait and thex(t)- andy(t)-graphsfor the solutions with the indicated initial conditions:

birmudah triangle is scaelenn

answer: the prove is mentioned below.

step-by-step explanation:

an isometric rigid transformation is a transformation of the plane that preserves lengths and angles.    

that is, the pre-image and the image under a rigid transformation will be congruent.

here, given: cb ║ ed and cb ≅ ed

prove that: δ cbf ≅ δ edf

since, cb ║ ed

therefore, by the alternative interior angle theorem,

∠fcb ≅ ∠fed

∠fbc ≅ ∠ fde

and, cb ≅ ed ( given)

therefore, the angles and sides are persevered after transformation.

thus, by the definition of isometric rigid transformation,

δ cbf ≅ δ edf