What are some effective stretching and warm up exercises for beginners before strength training

Stretching:

Quadriceps stretch: Stand with feet shoulder-width apart, holding one leg bent behind. Grab your foot and pull your heel towards your buttocks.
Hamstring stretch: Sit with legs extended forward, toes pointed. Reach forward and grab your toes, keeping your back straight.
Calf stretch: Stand with feet flat on the floor, knees slightly bent. Step forward with one leg and bend your back knee until you feel the stretch in your calf.
Shoulder stretch: Stand with feet shoulder-width apart, arms extended to the sides at shoulder height. Roll your arms forward in a circular motion.

Warm-up:

Jumping jacks: Stand with feet together and arms at your sides. Jump your feet out to shoulder-width and simultaneously raise your arms overhead. Jump back to starting position.
High knees: Stand with feet shoulder-width apart. Bring your right knee to your chest, then switch legs and repeat.
Arm swings: Stand with feet shoulder-width apart, feet flat on the floor. Swing your arms forward and backward in a circle.
Trunk rotations: Stand with feet shoulder-width apart, knees slightly bent. Rotate your torso from side to side.

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