Using the component form to add two vectors literally means adding the components of the vectors to create a new vector. For example, let a and b be two two-dimensional vectors. These vectors can be written in terms of their components.
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Suppose c is the sum of these two vectors, so that c = a + b. This means that formula_7.
Here is an example of addition of two vectors, using their component forms:
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This method works for all vectors, not just two dimensional ones.
The dot product is one method to multiply vectors. It produces a scalar. It uses component form:
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The cross product is another method to multiply vectors. Unlike dot product, it produces a vector. Using component form:
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Here, formula_13 means the length of formula_14, and formula_15 is the unit vector at right angles to both formula_14 and formula_17.
To multiply a vector by a scalar (a normal number), you multiply the number by each component of the vector:
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An example of this is
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Soap bubble
A soap bubble is a very thin film of soap water. Their shape is a hollow, round ball, or sphere. They have a colorful surface. Soap bubbles do not last very long. Sometimes they break in the air. When they touch something else, they usually break. When people talk about soap bubbles they think about them being pretty but short-lived. So, they are a symbol for other things that are pretty but short-lived or unimportant. Children enjoy playing with bubbles. Sometimes, adults enjoy seeing art done with soap bubbles.
They get their colors from iridescence.
Fire Brigades Union
The Fire Brigades Union (FBU) is the main union for firefighters in the United Kingdom. A union is a group of workers. They make the group to improve pay and working conditions. It was founded in 1918 in the London area as the "Firemans Trade Union". It soon grew to cover the entire country. Today, it has around 50,000 members.
Bicycle
A bicycle (or bike) is a small, human powered land vehicle with a seat, two wheels, two pedals, and a metal chain connected to cogs on the pedals and rear wheel. A frame gives the bike strength, and the other parts are attached to the frame. The name comes from these two words - the prefix "bi-" meaning two, and the suffix "-cycle" meaning wheel. It is powered by a person riding on top, who pushes the pedals around with his or her feet.
Riding bicycles, which is also called cycling, is an important way to travel in several parts of the world. The most popular type of cycling is Utility cycling. It is also a common recreation, a good form of low-impact exercise, and a popular sport. Road bicycle racing is the second most popular spectator sport in the world.
Bicycling uses less energy per mile than any other human transport.
In 1817 a German professor, Baron Karl von Drais, created the first two-wheeled bicycle. It was made of wood and had two wheels. The front wheel could be turned using the handlebars in order to steer the bike. However, it did not have pedals, so the rider would have to push their feet on the ground to make it move.
In the 1860s, French inventors added pedals to the front wheel. However, it took a lot of effort to turn the pedals. Later inventors made bikes out of metal only, and made the front wheel very big, giving higher speed. This design was called the penny-farthing bicycle. However, it was difficult to ride, since it could fall easily and the rider would fall far.
Several improvements were made in the 1880s and '90s. In 1885, the safety bicycle was invented. This had two wheels the same size so that the rider could sit at a lower height. It was called the safety bicycle because it much easier to ride than the penny-farthing. When stopping, the rider can simply put down a foot instead of completely dismounting. Instead of pedaling and steering with the front wheel, the safety bicycle steers with the front wheel while the pedals turn the back wheel using a chain. Brakes operated by hand levers on some bikes also increased safety.
In 1888, Scottish inventor John Boyd Dunlop re-invented a type of tire which was filled with air. This made safety bicycles more comfortable. Soon, the freewheel was invented. This was a device inside the hub of the back wheel that allowed the wheel to spin even if the rider wasn't pedaling. However, this meant the rider could no longer stop the bike by backpedaling. As a result, better hand brakes were invented, and a different type of brake which could stop the bike if the pedals were turned backwards. Later inventions included better brakes, and gears which made cycling over hills much easier. During this time the bicycle became very popular.
Basic components common to most bikes include a seat, pedals, gearing, handlebar, wheels, and brakes, all mounted on a frame. The majority also have a gear shifter. The cyclist's feet push the pedals to make them go around in circles, which moves the chain, which turns the back wheel of the bike to make the bike move forwards. The front wheel is connected to the handlebar, so turning the handlebar from side to side swivels the front wheel which steers the bike.
Many thousands of people are hurt every year in bicycle accidents, and hundreds die. Careful riding helps prevent accidents. When riding on streets, it is safest to ride on the same side of the street that cars drive (which would mean riding on the right side of the road in countries where people drive on the right side of the road, and riding on the left in countries where people drive on the left). To avoid hitting people, riders must obey signs that say "no bicycling", even if it does not seem to make sense at the time. Low light makes bicycle lighting important. It may not be safe to ride when it is dark. Riders wear reflective clothing to be safer in low light. Wearing a helmet makes bicycle riding safer. Wearing a helmet does not mean that somebody cannot be hurt if they crash their bicycle, but it makes being hurt less likely. Some bicycles have bells or horns that the rider can use to warn other people that they are riding by them.
Many places have a bicycle path linking houses with shops, schools and stations. These make bicycling safer, letting cyclists stay away from busy motor traffic on dangerous roads.
Wheel
A wheel is a disc or circle-shaped mechanical device. Its main purpose is to allow things to "roll"; in other words, the wheel spins, and object on the wheels moves more easily along the ground. It is a simple machine.
Most land vehicles roll on wheels. Wheels are often used in pairs, connected by a rod of wood or metal known as an axle. Many machines have wheels with teeth, known as gears. The principle behind the wheel is that of mechanical advantage.
This is a machine in which the wheel and axle turn together. It is the basis of many machines, not just vehicles. The potter's wheel, the lathe and the windlass are examples.
Most experts believe that the ancient Mesopotamians invented the wheel about 4000 BC.
People in Asia also discovered it on their own around 3500 BC. The Inca and Maya had wheels on children's toys around 1500 BC, but they did not use wheels for work. Africa south of the Sahara desert, Europe, and Australia did not have the wheel until people there met people from Europe. Early wheels were solid disks; the spoked wheel was invented around 2000 BC. The earliest documentation of a vehicle with wheels is a painting dated between 33503500 BC.
Physical exercise
The word exercise means:
People do physical exercises as a part of their healthy lifestyle to get stronger and healthier or stay strong and healthy or to improve their body image. There are three basic modes of physical exercises:
Exercises can be an important part of physical therapy, weight loss, or sports performance.