1.
Equator
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The Equator usually refers to an imaginary line on the Earths surface equidistant from the North Pole and South Pole, dividing the Earth into the Northern Hemisphere and Southern Hemisphere. The Equator is about 40,075 kilometres long, some 78. 7% lies across water and 21. 3% over land, other planets and astronomical bodies have equators similarly defined. Generally, an equator is the intersection of the surface of a sphere with the plane that is perpendicular to the spheres axis of rotation. The latitude of the Earths equator is by definition 0° of arc, the equator is the only line of latitude which is also a great circle — that is, one whose plane passes through the center of the globe. The plane of Earths equator when projected outwards to the celestial sphere defines the celestial equator, in the cycle of Earths seasons, the plane of the equator passes through the Sun twice per year, at the March and September equinoxes. To an observer on the Earth, the Sun appears to travel North or South over the equator at these times, light rays from the center of the Sun are perpendicular to the surface of the Earth at the point of solar noon on the Equator. Locations on the Equator experience the quickest sunrises and sunsets because the sun moves nearly perpendicular to the horizon for most of the year. The Earth bulges slightly at the Equator, the diameter of the Earth is 12,750 kilometres. Because the Earth spins to the east, spacecraft must also launch to the east to take advantage of this Earth-boost of speed, seasons result from the yearly revolution of the Earth around the Sun and the tilt of the Earths axis relative to the plane of revolution. During the year the northern and southern hemispheres are inclined toward or away from the sun according to Earths position in its orbit, the hemisphere inclined toward the sun receives more sunlight and is in summer, while the other hemisphere receives less sun and is in winter. At the equinoxes, the Earths axis is not tilted toward the sun, instead it is perpendicular to the sun meaning that the day is about 12 hours long, as is the night, across the whole of the Earth. Near the Equator there is distinction between summer, winter, autumn, or spring. The temperatures are usually high year-round—with the exception of high mountains in South America, the temperature at the Equator can plummet during rainstorms. In many tropical regions people identify two seasons, the wet season and the dry season, but many places close to the Equator are on the oceans or rainy throughout the year, the seasons can vary depending on elevation and proximity to an ocean. The Equator lies mostly on the three largest oceans, the Pacific Ocean, the Atlantic Ocean, and the Indian Ocean. The highest point on the Equator is at the elevation of 4,690 metres, at 0°0′0″N 77°59′31″W and this is slightly above the snow line, and is the only place on the Equator where snow lies on the ground. At the Equator the snow line is around 1,000 metres lower than on Mount Everest, the Equator traverses the land of 11 countries, it also passes through two island nations, though without making a landfall in either. Starting at the Prime Meridian and heading eastwards, the Equator passes through, Despite its name, however, its island of Annobón is 155 km south of the Equator, and the rest of the country lies to the north

2.
Zero S
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The Zero S is an electric motorcycle made by Zero Motorcycles. On 23 April 2009 the company announced it would establish a network in the Canadian market while getting regulatory approval for selling the motorcycle in Canada. It expects to start selling in Canada by early July 2009, the 2009 Zero S had an expected range of 81-kilometre on a full charge, with a top speed of 112 km/h, a speed it can reach in under four seconds from a standing start. The motor is rated at 22 kilowatts, the battery can be recharged using standard 110 V or 220 V plugs. A replacement battery will cost approximately $3,000, the 2014 range of Zero S have brought various improvements and the option for a powertank accessory which increases the range by 2. 8kWh. The 2015 model added ABS brakes and 2016 brought an increase to the battery size

3.
Vector bundle
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Such vector bundles are said to be trivial. A more complicated class of examples are the tangent bundles of smooth manifolds, tangent bundles are not, in general, trivial bundles, for example, the tangent bundle of the sphere is non-trivial by the hairy ball theorem. In general, a manifold is said to be parallelizable if, vector bundles are almost always required to be locally trivial, however, which means they are examples of fiber bundles. Also, the spaces are usually required to be over the real or complex numbers. Complex vector bundles can be viewed as real vector bundles with additional structure, in the following, we focus on real vector bundles in the category of topological spaces. The open neighborhood U together with the homeomorphism φ is called a trivialization of the vector bundle. The local trivialization shows that locally the map π looks like the projection of U × Rk on U, every fiber π−1 is a finite-dimensional real vector space and hence has a dimension kx. The local trivializations show that the function x ↦ kx is locally constant, if kx is equal to a constant k on all of X, then k is called the rank of the vector bundle, and E is said to be a vector bundle of rank k. Often the definition of a vector bundle includes that the rank is well defined, vector bundles of rank 1 are called line bundles, while those of rank 2 are less commonly called plane bundles. The Cartesian product X × Rk, equipped with the projection X × Rk → X, is called the trivial bundle of rank k over X and these are called the transition functions of the vector bundle. The set of transition forms a Čech cocycle in the sense that g U U = I, g U V g V W g W U = I for all U, V, W over which the bundle trivializes. Thus the data defines a bundle, the additional data of the gUV specifies a GL structure group in which the action on the fiber is the standard action of GL. Conversely, given a fiber bundle with a GL cocycle acting in the way on the fiber Rk. This is sometimes taken as the definition of a vector bundle, note that g is determined by f, and f is then said to cover g. The class of all vector bundles together with bundle morphisms forms a category, restricting to vector bundles for which the spaces are manifolds and smooth bundle morphisms we obtain the category of smooth vector bundles. Vector bundle morphisms are a case of the notion of a bundle map between fiber bundles, and are also often called bundle homomorphisms. A bundle homomorphism from E1 to E2 with an inverse which is also a homomorphism is called a bundle isomorphism. An isomorphism of a vector bundle E over X with the bundle is called a trivialization of E