Is it possible to have a net torque when all of the forces sum to zero? explain.

Yes it is possible

Explanation:

When two equal magnitude forces are acting on the rod in opposite direction

Then the net force on the system is always zero in that case

so we will have

now for the system net torque due to these forces is given by

here we know that

= distance of the forces from reference about which torque is measured

so here we can say that net force is zero on the system while torque is not zero

in all such case object will rotate about a fixed position with change angular speed

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)