Mechanical properties of carbon nanotubes Mechanical properties of carbon nanotubes The mechanical properties of carbon nanotubes reveal them as one of the strongest materials in nature. Carbon nanotubes (CNTs) are long hollow cylinders of graphene. Although graphene sheets have 2D symmetry, carbon nanotubes by geometry have different properties in axial and radial directions. It has been shown that CNTs are very strong in the axial direction. Young's modulus on the order of and tensile strength of were obtained. Carbon nanotubes are the strongest and stiffest materials yet discovered in terms of tensile strength and elastic modulus respectively. This strength results from the covalent sp bonds
Rotations and reflections in two dimensions Rot(−"φ"). Every reflection Ref("θ") is its own inverse. Composition has closure and is associative, since matrix multiplication is associative. Notice that both Ref("θ") and Rot("θ") have been represented with orthogonal matrices. These matrices all have a determinant whose absolute value is unity. Rotation matrices have a determinant of +1, and reflection matrices have a determinant of −1. The set of all orthogonal two-dimensional matrices together with matrix multiplication form the orthogonal group: "O"(2). Rotations and reflections in two dimensions In geometry, two-dimensional rotations and reflections are two kinds of Euclidean plane isometries which are related to one another. A rotation