On a certain map, every 2 cm represents 10 km on Earth's surface. Which ratio represents the scale of the map, which shows how the map
measurements compare to actual ones on Earth's surface?

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

continuous conducting path for current, power supply

conduct current i mean it makes sense