Q: Does the word "give" mean the same thing in "Give one's opinion." and "Give an excuse."?

A: the same meaning

Q: Does the word "stretch" mean the same thing in "During the Inquisition, the torturers would stretch their victims on a rack." and "Let's stretch for a minute -- we've been sitting here for over 3 hours."?

A: different meanings

Q: Does the word "optimization" mean the same thing in "To promote the optimization and diversification of agricultural products." and "In an optimization problem we seek values of the variables that lead to an optimal value of the function that is to be optimized."?

A: the same meaning

Q: Does the word "bit" mean the same thing in "A horse hates having a bit put in its mouth." and "The horse was not accustomed to a bit."?

A:
the same meaning