Imports System.Drawing, System.Drawing.Drawing2D

Public Class Affine
    Dim mat As Matrix
    ''' <summary>
    ''' X value of translation vector.
    ''' </summary>
    ''' <value></value>
    ''' <returns></returns>
    ''' <remarks></remarks>
    Public ReadOnly Property offsetx() As Single
        Get
            Return mat.OffsetX
        End Get
    End Property
    ''' <summary>
    ''' Y value of translation vector.
    ''' </summary>
    ''' <value></value>
    ''' <returns></returns>
    ''' <remarks></remarks>
    Public ReadOnly Property offsety() As Single
        Get
            Return mat.OffsetY
        End Get
    End Property

    ''' <summary>
    ''' rotation in degrees, clockwise = positive
    ''' </summary>
    ''' <remarks></remarks>
    Public rot As Single

    ''' <summary>
    ''' x and y values of scale vector
    ''' </summary>
    ''' <remarks></remarks>
    Public scalex, scaley As Single
    ''' <summary>
    ''' x and y values of shear vector
    ''' </summary>
    ''' <remarks></remarks>
    Public shearx, sheary As Single

    ''' <summary>
    ''' Construct a new Affine from the given Drawing2d.Matrix
    ''' </summary>
    ''' <param name="m"></param>
    ''' <remarks></remarks>
    Sub New(ByVal m As Matrix)
        mat = m
        Decompose()
    End Sub

    ''' <summary>
    ''' Create a new Affine with default values (corresponding to identity matrix)
    ''' </summary>
    ''' <remarks></remarks>
    Sub New()
        mat = New matrix
        rot = 0
        scalex = 1
        scaley = 1
        shearx = 0
        sheary = 0
    End Sub

    ''' <summary>
    ''' Decompose our matrix
    ''' </summary>
    ''' <remarks></remarks>
    Private Sub Decompose()

        ' the original matrix
        Dim m0 As Matrix = mat

        ' remove translation
        Dim m1 As New Matrix
        m1.Multiply(m0)
        m1.Translate(-m0.OffsetX, -m0.OffsetY)

        ' get rotation
        Dim pts(1) As PointF
        pts(0) = New PointF(0, 0)
        pts(1) = New PointF(1, 0)
        m1.TransformPoints(pts)
        rot = Math.Atan2( _
            pts(1).Y - pts(0).Y, _
            pts(1).X - pts(0).X) * 180.0 / Math.PI

        ' get scale and shear
        pts(0) = New PointF(0, 0)
        pts(1) = New PointF(1, 1)
        Dim m2 As New Matrix
        m2.Rotate(-rot)
        m2.Multiply(mat)
        m2.TransformPoints(pts)

        scalex = pts(1).X - pts(0).X
        scaley = pts(1).Y - pts(0).Y

        ' get shear
        shearx = pts(1).X - 1.0
        sheary = pts(1).Y - 1.0

    End Sub

    'Sub test()
    '    Dim m As New Matrix
    '    Dim a As New Affine(m)
    '    Assert.AreEqual(0.0, a.rot)
    '    Assert.AreEqual(1.0, a.scalex)
    '    Assert.AreEqual(1.0, a.scaley)
    '    Assert.AreEqual(0.0, a.shearx)
    '    Assert.AreEqual(0.0, a.sheary)

    '    m.Rotate(45)
    '    m.Scale(2, 3)
    '    a = New Affine(m)
    '    Assert.AreEqual(45.0, a.rot)
    '    Assert.Less(Math.Abs(2.0 - a.scalex), 0.001)
    '    Assert.Less(Math.Abs(3.0 - a.scaley), 0.001)

    'End Sub
End Class

Thanks to some messages on CodeProject.com for the final answers, here assembled in one place

Get translation, rotation, scale and shear out of a System.Drawing.Drawing2d.Matrix affine transformation

VB.NET