Both Uses of

resolution

in

Unbroken, by Hillenbrand

Though exhausted, they fought the urge to sleep, afraid that a ship or submarine would pass and they'd miss it. ... Mac was alone in his wakefulness, his mind spinning with fear. ... Grasping at an addled resolution, he began to stir.
p. 130.9 *

resolution = determination (firmness of purpose)

Through tears, he apologized and promised never to mistreat another POW. His resolution didn't last.
p. 236.5 *

resolution = firm decision to do something

Definitions:

(1) (resolution as in: a New Year's resolution)
a firm decision to do something
(2) (resolution as in: a United Nations resolution)
a formal statement of decision or opinion voted on by a group

While a resolution typically expresses an opinion and has no legal force, when used in early U.S. history or in the expressions joint resolution of Congress or continuing resolution, it becomes a synonym for legislation (meaning that it carries the force of law).
(3) (resolution as in: Her resolution weakened.)
determination (firmness of purpose)
(4) (resolution as in: resolution of the dispute)
a solution or outcome
(5) (meaning too rare to warrant focus)
Much less commonly, other meanings of resolution include:
- a measure of optic detail -- as in: "The photograph has excellent resolution."
- separation into different parts -- as in: "When force is applied to an inclined plane there is resolution of the force into horizontal and vertical components."
- conversion to something else -- as in: "... resolution of the chord from dissonance (an unstable sound) to consonance (a more stable sound)."
- reduction to or conversion to something else -- as in: "It permits resolution of a URL to an IP address."