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Greatest distance between any two points in the 50 states: 5,859 miles (9,429 km), from Kure Atoll, Hawaii, to Log Point, Elliott Key, Florida. [23] Greatest distance between any two points in the contiguous 48 states: 2,901 miles (4,669 km), from North Farallon Island, California, to Sail Rock, east of West Quoddy Head, Maine. [23]
The longest continuous north–south distance on land is 7,590 km (4,720 mi) along the meridian 99°1'30"E, from the northern tip of Siberia in the Russian Federation (76°13′6″N 99°1′30″E / 76.21833°N 99.02500°E / 76.21833; 99.02500. ), through Mongolia, China, and Myanmar, to a point on the south coast of Thailand (7 ...
California. 42°00′34″N 122°22′41″W / 42.00944°N 122.37806°W / 42.00944; -122.37806. Oregon border northeast of Hornbrook. 32°32′04″N 117°07′26″W / 32.53444°N 117.12389°W / 32.53444; -117.12389. Baja California border where it meets the Pacific Ocean in Border Field State Park.
Definition. The trace distance is defined as half of the trace norm of the difference of the matrices: where is the trace norm of , and is the unique positive semidefinite such that (which is always defined for positive semidefinite ). This can be thought of as the matrix obtained from taking the algebraic square roots of its eigenvalues.
Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
The Chebyshev distance between two vectors or points x and y, with standard coordinates and , respectively, is. This equals the limit of the L p metrics: hence it is also known as the L ∞ metric. Mathematically, the Chebyshev distance is a metric induced by the supremum norm or uniform norm. It is an example of an injective metric.