A map has been drawn using a scale of 1:10 000. What does 1 cm on the map represent in reality? Which of the following is a vector quantity: volume, time, weight, velocity?

Here are the solutions to the questions from the image: Question 1: A map has been drawn of the local area using a scale of 1: 10 000. What does a distance of 1 cm on the map represent a real distance of? Step 1: Understand the map scale. A scale of 1:10 000 means that 1 unit on the map corresponds to 10 000 units in real life. Step 2: Calculate the real distance in centimeters. If 1 cm on the map, then the real distance is 1 cm × 10 000 = 10 000 cm. Step 3: Convert the real distance to a more practical unit (meters). Since 1 m = 100 cm: 10 000 cm = (10 000)/(100) m = 100 m A distance of 1 cm on the map represents a real distance of 100 m. Question 2: Which of the following is a vector quantity? volume, time, weight, velocity. A vector quantity is a physical quantity that has both magnitude and direction. Volume has magnitude but no direction (scalar). Time has magnitude but no direction (scalar). Weight is a force, which has both magnitude and direction (vector). Velocity has both magnitude (speed) and direction (vector). Among the given options, both weight and velocity are vector quantities. However, in typical multiple-choice scenarios asking for "a" vector quantity, velocity is a very common and direct example. The vector quantity is velocity. Question 3: Quantities that may be specified simply by giving their magnitude are called ____ quantities. Quantities that are defined only by their magnitude are known as scalar quantities. The quantities are called scalar. Question 4: Two vectors a and b are equal if and only if they have ____ magnitude and direction. For two vectors to be considered equal, they must have the same magnitude and the same direction. Two vectors a and b are equal if and only if they have the same magnitude and direction. Question 5: Find vector x in terms of a and b. Step 1: Apply the triangle law of vector addition. The triangle law states that if two vectors are represented by two sides of a triangle taken in order, their resultant is represented by the third side taken in the opposite order. Step 2: Write the vector equation based on the diagram. In the given triangle, vector 'a' and vector 'b' are arranged head-to-tail. Vector 'x' is the resultant vector, starting from the tail of 'a' and ending at the head of 'b'. Therefore, vector x is the sum of vector a and vector b. x = a + b Vector x in terms of a and b is a + b. 3 done, 2 left today. You're making progress.